Mathematical Terminology

adverb to infinity; endlessly; without limit

• The mathematical sequence continues ad infinitum.
• We could talk about this topic ad infinitum.
• I could scroll through social media ad infinitum.
• His love for her seemed to stretch ad infinitum.

adjective used to refer to the whole quantity or extent of something

adverb completely; entirely

pronoun used to refer to the whole quantity or extent of something

• All employees are required to attend the mandatory training session.
• Let's all meet up for lunch later.
• We're all good to go for the concert tonight.
• She gave her all in the final performance.

adverb an adverb modifies a verb, adjective, or other adverb, indicating the time, place, degree, or manner of an action

preposition a preposition shows the relationship between a noun (or pronoun) and other words in a sentence

• The project is almost complete and ready for submission.
• I'm almost done with my homework, just a few more questions to go.
• I'm almost there, just hold on a little longer.
• His words were almost like a dagger to her heart.

verb The word 'am' is a form of the verb 'to be', specifically the first person singular present tense form.

• I am currently reviewing the report before submitting it to the board.
• I am going to the store later, do you need anything?
• I am so over this drama, I can't deal with it anymore.
• His determination to succeed is like a fire that never goes out, he is an unstoppable force.

noun a figure formed by two rays or lines that meet at a point

verb to move or bend in a particular direction or at a particular angle

• The architect carefully calculated the angle of the building's roof to ensure proper drainage.
• Can you adjust the angle of the camera so we can get a better view?
• I totally aced that math test, I had all the angles covered.
• She always approaches situations from a different angle, which is why she's so successful.

noun a word, phrase, or clause referred to by a pronoun

adjective preceding in time or order; previous or preexisting

• The researcher examined the antecedent factors that led to the economic downturn.
• I'm not sure what the antecedent was for his sudden change in behavior.
• She always seems to have some drama going on, but I never know the antecedent.
• In literature, the author often includes antecedents to provide background information on the characters.

noun A region or country on the opposite side of the globe

• The antipodes of a location refers to the exact opposite point on the Earth's surface.
• I heard that Australia is considered the antipodes of the United States.
• I can't believe we're going to the antipodes for vacation!
• In terms of personality, they are like antipodes - complete opposites.

noun a person or thing that is the exact opposite or contrary of another

• The antipole of a point on the Earth's surface is the point on the opposite side of the planet.
• If you dig a hole straight through the Earth, you'll end up at the antipole.
• I heard that if you go to the antipole, you'll find a secret underground city.
• In terms of personality, they are like the antipole of each other.

adjective used to refer to one or some of a thing or things, no matter how much or how many

pronoun used to refer to one or some of a thing or things, no matter how much or how many

• Please let me know if you have any questions regarding the project.
• Do you have any plans for the weekend?
• I don't have any clue what you're talking about.
• She didn't show any signs of weakness during the competition.

verb to divide and allocate something in portions or shares

• The committee had to apportion the budget among various departments.
• Let's apportion the tasks evenly so no one feels overwhelmed.
• I'll apportion the snacks for the road trip.
• She had to apportion her time wisely between work and family responsibilities.

verb moving closer to a particular place or person

adjective coming near or drawing close in time or distance

• The deadline for submitting the project proposal is quickly approaching.
• Hey, did you know that our lunch break is approaching?
• I can't believe the party is already approaching, time flies!
• As she walked through the forest, she felt a sense of unease approaching.

noun a rough estimate or calculation

adjective approximately correct

• The scientist used mathematical approximation to estimate the value of the constant.
• Can you give me a rough approximation of how much this will cost?
• I'm just gonna ballpark it and give you an approximation.
• Her painting was not an exact replica of the scene, but rather an approximation of it.

noun Not applicable

verb Not applicable

adjective Based on random choice or personal whim, rather than any reason or system.

adverb Not applicable

pronoun Not applicable

preposition Not applicable

conjunction Not applicable

interjection Not applicable

article Not applicable

• The judge made an arbitrary decision based on insufficient evidence.
• She just picked a random number, it was so arbitrary.
• The rule is totally arbitrary, it makes no sense.
• The artist's use of color was arbitrary, adding a sense of chaos to the painting.

adjective relating to or involving arithmetic, the branch of mathematics that deals with the properties and manipulation of numbers

• The professor taught us about arithmetical operations in our advanced mathematics class.
• I struggle with arithmetical calculations, I always need a calculator.
• I'm terrible at arithmetical stuff, it's just not my thing.
• The arithmetical precision of his arguments left no room for doubt.

adverb used to indicate movement in a circular direction or to indicate proximity or location

preposition used to indicate movement in a circular direction or to indicate proximity or location

• The committee gathered around the conference table to discuss the budget.
• Let's meet around 6 pm for dinner at the new restaurant.
• We should hang around the park after school.
• She felt like her world was crumbling around her.

verb present participle of the verb ascend, meaning to move or go upwards

adjective describing something moving or going upwards

• The hikers began their ascending journey up the mountain.
• We're going to start ascending the hill soon.
• Let's start climbing up, it's time to ascend!
• Her career has been steadily ascending over the past few years.

adjective not identical on both sides of a central line; lacking symmetry

• The company's financial report showed an asymmetric distribution of profits among its subsidiaries.
• The team noticed an asymmetric pattern in the data they were analyzing.
• Her haircut is so asymmetric, it's really edgy and cool.
• Their relationship was becoming increasingly asymmetric, with one person giving much more than the other.

noun a straight line that a curve approaches but never crosses or touches

verb not applicable

adjective not applicable

adverb not applicable

pronoun not applicable

preposition not applicable

conjunction not applicable

interjection not applicable

article not applicable

• The curve approaches the asymptote but never actually touches it.
• The line gets really close to the asymptote but doesn't quite reach it.
• The graph is like, almost touching the asymptote but not really.
• Their relationship was like an asymptote, always getting close but never quite connecting.

adverb modifying a verb, adjective, or other adverb to indicate time, place, manner, or degree

preposition a word that shows the relationship between a noun (or pronoun) and other words in a sentence

• The results of the two studies were at variance with each other.
• Their opinions were at variance so they couldn't agree on a solution.
• Their tastes in music were totally at variance - they couldn't agree on a single song.
• Their paths in life were at variance, leading them in different directions.

noun a statement or proposition that is regarded as being established, accepted, or self-evidently true

• In mathematics, an axiom is a statement that is taken to be true without proof.
• The basic axiom of economics is that people respond to incentives.
• I live by the axiom 'treat others how you want to be treated'.
• The golden rule can be seen as a moral axiom in many cultures.

noun a self-evident truth that requires no proof

adjective self-evident or unquestionable

• In mathematics, it is axiomatic that a straight line is the shortest distance between two points.
• It's axiomatic in our family that breakfast is the most important meal of the day.
• It's like, axiomatic that you gotta hustle to make it in this city.
• For her, trust was axiomatic - once broken, it could never be fully restored.

noun a straight line about which a body or a geometric figure rotates or may be supposed to rotate

• The Earth rotates on its axis, causing day and night.
• Make sure you align the wheels properly on the axis before tightening the bolts.
• I can't believe she's still hung up on her ex, she needs to get off that axis.
• The new policy shift will serve as a central axis for our future business strategies.

noun the underlying support or foundation for an idea, argument, or process

• The company reviews its financial statements on a quarterly basis.
• I check my email on a daily basis.
• I hit the gym on a regular basis to stay in shape.
• Trust is the basis of any healthy relationship.

noun a curved or angular deviation from a straight line or course

verb to cause to curve or deviate from straightness

• The road took a sharp bend to the left.
• I had to bend down to pick up the pen from the floor.
• She can bend it like Beckham when she kicks the ball.
• Sometimes you have to bend the rules in order to get things done.

noun a division into two branches or parts

• The river's bifurcation created two separate streams flowing in different directions.
• The road's bifurcation confused me, I didn't know which way to go.
• I hate this stupid bifurcation, it's so annoying!
• The decision to leave his job marked a bifurcation in his career path.

noun a mathematical expression consisting of two terms

adjective relating to or consisting of two terms

• The binomial theorem is a fundamental concept in algebra.
• I had to study the binomial thing for my math test.
• I don't get this binomial stuff, it's too confusing.
• Life is like a binomial equation, with ups and downs balancing each other out.

verb to divide into two equal parts

• The mathematician used a ruler and compass to accurately bisect the line segment.
• I watched as my friend tried to bisect the cake perfectly down the middle.
• I totally bisected that argument with my killer comeback.
• The river seemed to bisect the forest, dividing it into two distinct halves.

noun a container typically made of wood or cardboard, used for storing or transporting items

verb to confine or enclose within a space or boundaries

• Please make sure to box in the fragile items before shipping them.
• Hey, can you box in those breakable things before we move?
• Yo, make sure to box in the delicate stuff before we haul it.
• It's important to box in your emotions and not let them control you.

adjective able to be calculated or estimated

• The exact cost of the project is not easily calculable due to various factors.
• It's hard to figure out the total cost of the project since there are so many variables.
• Trying to crunch the numbers for this project is a real headache.
• The impact of his actions on the company's reputation is incalculable.

verb to determine or estimate by using mathematical or numerical methods

• It is important to calculate on accurate data when making financial projections.
• Make sure you calculate on the right numbers before finalizing your budget.
• Don't just guess, calculate on the real figures to be sure.
• In order to succeed, you must calculate on the strengths and weaknesses of your competitors.

verb to determine or ascertain by mathematical methods; compute

• In order to determine the total cost, we need to calculate the expenses incurred.
• Let's calculate how much each person needs to chip in for the dinner bill.
• I'm terrible at math, can you calculate this for me?
• Sometimes it's hard to calculate the true value of a friendship.

verb to determine or estimate something based on mathematical or logical reasoning

• The scientist carefully calculated the precise measurements needed for the experiment.
• I calculated how much money I would need for the trip and it's more than I expected.
• I calculated that party would be lit, so I made sure to RSVP.
• She calculated the risks of starting her own business and decided it was worth it.

noun a mathematical determination of the size or number of something

adjective relating to or involving calculations

• The calculation of the company's annual revenue requires a thorough analysis of financial statements.
• I did the calculation for splitting the bill at the restaurant last night.
• I'm terrible at math, so I always use a calculator for any calculations I need to do.
• The calculation of risk versus reward is crucial in making investment decisions.

noun a monetary unit equal to one hundredth of a dollar or other unit of currency

• The cost of the new equipment is one hundred cents.
• I only have fifty cents left for the bus fare.
• I'm broke, I don't have a cent to my name.
• His ideas are worth a cent in today's market.

verb to restrict or limit within certain boundaries or lines

• The boundaries of the property are circumscribed by a tall fence.
• We can only play within the circumscribed area of the park.
• Don't circumscribe me with your rules, let me live my life.
• His fear of failure circumscribed his ability to take risks and try new things.

noun A quantity or factor that measures a certain property or characteristic.

adjective Describing something related to coefficients.

• The coefficient of determination is a measure of how well the regression line fits the data points.
• You can think of the coefficient as a sort of 'multiplier' that helps us understand the relationship between variables.
• The coefficient basically tells us how much one thing affects another in a math equation.
• In this equation, the coefficient is like the conductor of an orchestra, directing how all the variables play together.

verb to extend or stretch out together in the same direction

• The two principles coextend throughout the entire organization.
• Their responsibilities coextend to cover all areas of the project.
• Our friendship coextends beyond just hanging out.
• The impact of his actions coextends to affect everyone around him.

verb to occur at the same time or place; to correspond exactly

• The dates of the conference will coincide with the national holiday.
• Our vacation plans happen to coincide with the music festival in town.
• It's crazy how our schedules just happened to coincide like that.
• Their interests coincided perfectly, like pieces of a puzzle fitting together.

adjective describing something that happens by chance or at the same time as something else

• The timing of their arrival was purely coincident with the start of the meeting.
• It was just coincident that we both ended up at the same restaurant last night.
• What a crazy coincident that we both got the same grade on the test!
• Their paths crossing was no mere coincident, but a sign of fate at work.

verb Coinciding is the present participle form of the verb coincide, which means to occur at the same time or to correspond in nature.

adjective Coinciding can also function as an adjective, describing something that is happening at the same time or in agreement with something else.

• The project deadline is coinciding with the annual company meeting.
• My birthday is coinciding with the long weekend, so I'm planning a trip.
• I can't believe our plans are coinciding, what are the odds?
• Her happiness was coinciding with the arrival of spring.

noun a joining or merging of different elements to form a whole

adjective describing something that is made up of different parts or elements

• The research study found that a combination of factors contributed to the overall success of the project.
• I love the combination of flavors in this dish - it's so delicious!
• That outfit is a killer combination, you look amazing!
• In literature, the author often uses a combination of symbolism and imagery to convey deeper meanings in the text.

noun a combination of two or more things

verb to bring or join together in a single place or thing

adjective made by putting two or more things together

• The two companies decided to merge and their combined efforts led to increased profits.
• When we work together, our skills are combined and we can achieve great things.
• We make a great team when our talents are combined.
• The flavors of chocolate and peanut butter combined create a delicious treat.

noun a building or group of buildings with a specific purpose

adjective consisting of many different and connected parts

• The research project involved analyzing complex data sets to draw meaningful conclusions.
• The math problem was so complex, I had no idea where to start.
• Dude, that game is way too complex for me to figure out.
• Her emotions were a complex web of conflicting feelings.

noun a noun is a person, place, thing, or idea. In this case, 'concavity' is a noun referring to the quality of being concave or having a surface that curves inward.

• The concavity of the parabola can be determined by looking at the sign of the coefficient of the x^2 term.
• The concavity of this graph makes it look like a smiley face.
• The concavity of the road ahead is no joke, so drive carefully.
• Her concavity towards authority figures was evident in the way she always followed the rules.

noun the state or quality of being in agreement or harmony

adjective congruent; in agreement or harmony

• The congruence of the two shapes was evident in the geometry problem.
• The congruence between their opinions made the decision easier.
• Their outfits were on point, showing congruence in their fashion sense.
• The congruence of their goals led to a successful partnership.

noun an opinion or conclusion formed on the basis of incomplete information

verb to form an opinion or supposition without sufficient evidence

• The scientist presented a conjecture based on the data collected from the experiment.
• I heard a wild conjecture about the new project at work.
• Don't listen to those baseless conjectures going around the office.
• Her conjecture about the future of the company turned out to be surprisingly accurate.

adjective describing something that follows in order or sequence without interruption

• The team won their third consecutive game in the tournament.
• We've had three consecutive days of rain now.
• I can't believe I've missed three consecutive parties.
• Her consecutive wins in the competition have boosted her confidence.

noun a situation or state of affairs that does not change

adjective occurring continuously over a period of time

• The speed of light is a constant in physics.
• She's always talking about her constant need for caffeine.
• My best friend is my constant, we do everything together.
• Change is the only constant in life.

noun the unbroken and consistent existence or operation of something over a period of time

adjective continuing without interruption

• The continuity of the research project was maintained throughout the entire study.
• We need to make sure there's continuity in our plans for the event.
• Let's keep the continuity going with our music playlist.
• The continuity of her thoughts was like a flowing river, never interrupted.

adjective forming an unbroken whole; without interruption

• The continuous improvement of our products is essential for maintaining our competitive edge.
• I can't believe the continuous rain we've been having lately.
• She's been on a continuous winning streak in the gaming tournament.
• The continuous flow of ideas in the brainstorming session was inspiring.

verb to come together from different directions and meet at a point

• The lines of the two equations will eventually converge at a single point.
• The two roads converge just up ahead, so we're almost there.
• Let's converge at the coffee shop later to discuss our project.
• The different opinions in the meeting started to converge towards a consensus.

noun a convex shape or surface

adjective having a surface or boundary that curves or bulges outward, as opposed to concave

• The convex shape of the lens focuses light onto the retina.
• The mirror is kind of convex, so it makes things look bigger.
• That convex curve is really cool, it gives the room a modern vibe.
• Her smile created a convex curve on her face, showing her happiness.

noun a person or thing that is equal in importance, rank, or quality

verb to organize or integrate elements in a harmonious way

• It is important to coordinate the schedules of all team members for the project to run smoothly.
• Let's coordinate with everyone to find a time that works for the meeting.
• We need to coordinate our outfits for the party tonight.
• The dancers moved in perfect coordinate with each other during the performance.

noun a proposition that follows from one already proved

adjective naturally following or resulting from

• The corollary of this theorem can be proven using a similar approach.
• The corollary to that is we'll have to find another way to solve the problem.
• The corollary of skipping class is getting detention.
• The corollary of taking risks is experiencing both success and failure.

noun a letter or email exchanged between people

verb to be similar or equivalent in character, form, or function

• Please correspond with the client to confirm the meeting details.
• Make sure to correspond with your roommate about cleaning the kitchen.
• I'll correspond with my friend to figure out our plans for the weekend.
• The colors in the painting correspond beautifully with each other.

verb present participle of correspond, which means to have a close similarity, connection, or equivalence

adjective relating to or in agreement with something else

• The corresponding data points on the graph show a clear correlation.
• Make sure to match the corresponding answers with the questions.
• I need to find the right emoji that corresponds with my mood.
• His actions did not correspond with his words, showing a lack of integrity.

noun a device used to keep count of something, typically a mechanical or electronic one used in various games and sports

verb to speak or act in opposition to

• The cashier behind the counter greeted the customer with a smile.
• I'll meet you by the counter at the front of the store.
• Let's grab some snacks at the counter before heading out.
• She used humor as a counter to his serious demeanor.

noun the action or process of determining the total number of something

verb to determine the total number of something by assigning numbers or numerals to individual items

• The accountant spent the entire day counting the company's financial transactions.
• I lost track of how many times I've been counting down the days until my vacation.
• I've been counting on my best friend to help me with my homework.
• She's always counting her blessings, no matter how tough things get.

noun a point at which a situation becomes very bad or very good

adjective having crucial importance or relevance

• In mathematics, a critical point is a point on a curve where the derivative is either zero or undefined.
• When you're graphing a function, look for the critical points to find where the function might have a maximum or minimum.
• Dude, that's the critical point where everything went wrong in our plan.
• Reaching a critical point in a relationship can either make it stronger or lead to a breakup.

noun a small, separate area in a larger room or space, often used for storage or as a workspace

adjective relating to or shaped like a cube; having three dimensions

• The cubical shape of the building allows for efficient use of space.
• I'll meet you by the cubical in the office.
• Let's hang out in the cubical after work.
• Her mind felt like a cubical, boxed in and lacking creativity.

verb to gather or pile up gradually over time

adjective forming a cumulative whole

• Over time, the company's profits will cumulate to a significant amount.
• If you keep saving a little bit each month, it will cumulate into a nice sum in the future.
• I didn't realize how much junk would cumulate in my garage over the years.
• The stress of work and personal life can cumulate and become overwhelming if not managed properly.

verb to prepare food using curry powder or spices

• The chef prepared a delicious curried chicken dish for the banquet.
• I love when my mom makes curried vegetables for dinner.
• Let's grab some curried rice from the food truck.
• The artist curried the colors on the canvas to create a vibrant masterpiece.

noun a line or outline that gradually deviates from being straight for some or all of its length

verb to bend or follow a curved path

• The mathematician plotted the curve on the graph to analyze its shape.
• I love driving on roads with lots of curves, it's so much fun!
• That skateboarder totally nailed the curve on that ramp!
• Life is full of unexpected curves, we just have to learn how to navigate them.

adjective relating to or characterized by cycles or recurrence

• The process follows a cyclic pattern, repeating every four weeks.
• I noticed a cyclic trend in the stock market, it seems to go up and down every few months.
• Dude, it's like a never-ending cycle, so cyclic!
• Her emotions were cyclic, fluctuating between extreme highs and lows.

noun A number expressed in a system of notation that uses a radix of 10, typically including a decimal point.

adjective Relating to or denoting a system of numbers and arithmetic based on the number ten.

• The result of the calculation is expressed as a decimal.
• Just give me the answer in decimal form.
• I can't deal with all these decimals, it's too much math for me.
• Her chances of winning were just a decimal compared to the competition.

verb to state or describe exactly the nature, scope, or meaning of something

• In academic writing, it is important to define key terms before delving into the discussion.
• Can you define what 'lit' means in this context?
• I can't believe you don't know what 'flex' means, let me define it for you.
• To me, success is defined by the impact you have on others rather than material wealth.

noun A word that refers to a person, place, thing, event, substance, or quality.

• The dictionary provides a clear definition of the word 'definition'.
• Can you give me a simple definition of this word?
• I need the lowdown on this - what's the definition?
• In literature, the author's use of symbolism can add a deeper definition to the story.

noun a person whose behavior or attitudes have declined to a lower standard

verb to decline or deteriorate in quality or value

• The scientist studied the effects of degenerate matter in the universe.
• I heard that guy is a degenerate gambler.
• Don't hang out with him, he's a total degenerate.
• The city's infrastructure has become degenerate over the years.

noun a name or symbol that represents something

verb to indicate or be a sign of something

• In academic writing, the term 'denote' is often used to indicate the literal meaning of a word.
• When I say 'denote', I mean it represents or stands for something specific.
• When we use 'denote' in this context, it's like saying 'this is what it really means'.
• The color red can denote both love and anger, depending on the context.

noun a mental disorder or disturbance

• The patient exhibited signs of cognitive derangement.
• She went through a period of emotional derangement after the breakup.
• His behavior was so deranged, it was like he was from another planet.
• The derangement of the original plan led to a complete restructuring of the project.

noun a financial product that derives its value from an underlying asset

adjective derived from another source

• The derivative of a function at a given point is the rate at which the function is changing at that point.
• I'm having trouble understanding how to find the derivative of this function.
• I totally bombed the quiz on derivatives today.
• The new product is a derivative of the original design, with some added features.

verb to obtain or receive from a source or origin

• Scientists derive conclusions from carefully conducted experiments.
• We can derive some useful information from this data.
• I'm trying to derive some fun out of this boring situation.
• She was able to derive strength from her past experiences.

verb Moving or falling downward

adjective Going or coming down

adverb In a descending manner

• The airplane began descending towards the airport.
• We are descending to the lower level now.
• Let's descend down to the basement for a while.
• As the sun set, a sense of darkness was descending upon the town.

adjective describes a quality or attribute of a noun, in this case, determinate describes something that is fixed or definite

• The determinate factor in this equation is the value of x.
• It's pretty determinate that we're going to the beach tomorrow.
• I'm determinate on getting that promotion at work.
• Love is not always determinate by logic or reason.

noun a simplified drawing showing the appearance, structure, or workings of something; a chart or plan

• The textbook includes a detailed diagram of the human respiratory system.
• I found a cool diagram online that explains how the internet works.
• Check out this sick diagram I made to show how the project will flow.
• Her speech painted a vivid diagram of the struggles she had overcome in her life.

noun a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.

• The diameter of the circle can be calculated by doubling the radius.
• The diameter of this pizza is huge!
• Check out the diameter of that burger, it's massive!
• The diameter of his influence in the industry is unparalleled.

verb to be unlike or dissimilar; to vary in opinion or belief

• The two theories differ in their approach to solving the problem.
• Their opinions differ on which movie is the best.
• Me and my friends always differ on where to eat for dinner.
• Their personalities couldn't be more different, they differ like night and day.

noun a difference between amounts of things; a distinction between similar things

adjective relating to or showing a difference

• The differential between the two interest rates is quite significant.
• There's a big differential in prices between the two stores.
• The price differential is like night and day.
• The differential in their personalities is what makes them such a dynamic duo.

noun the process of distinguishing or contrasting things

verb to recognize or express the difference between things; distinguish

• It is important to differentiate between fact and opinion when conducting research.
• I can't differentiate between these two brands of headphones; they both sound the same to me.
• I can never differentiate between the twins - they look exactly alike!
• Her unique style of painting really helps her differentiate herself from other artists.

noun the distinguishing of a difference

• The key to success in this market is effective product differentiation.
• If you want to stand out, you need to show some differentiation in your work.
• She really knows how to do her own thing and create some differentiation.
• In a world full of copies, be the differentiation that sets you apart.

noun a measurable extent of some kind, such as length, breadth, depth, or height

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• The architect carefully considered every dimension of the building before finalizing the design.
• I have no idea what the dimensions of this room are, but it looks pretty spacious.
• That car is next level, it's got some crazy dimensions going on.
• His storytelling added a new dimension to the classic tale.

adjective extending or moving from one place to another without changing direction or stopping

adverb in a straight line or by the shortest route

• The manager directly oversees all project activities.
• I'll talk to him directly about the issue.
• I'm gonna hit you up directly on your phone.
• Her words hit me directly in the heart.

verb to disturb the arrangement or order of something

adjective not arranged or put in order

• The documents on the desk were disarranged after the meeting.
• My room is disarranged because I couldn't find my keys this morning.
• I disarranged my outfit trying to find the perfect shoes to wear.
• Her thoughts were disarranged as she tried to make sense of the situation.

adjective Describing something that is not continuous or uninterrupted, having breaks or gaps

• The data showed a discontinuous pattern, indicating irregular intervals.
• The road construction caused a lot of discontinuous traffic.
• I can't stand his discontinuous texting habits.
• Her thoughts were like a discontinuous stream, jumping from one topic to another.

noun a separate or distinct entity

adjective separate or distinct

• The data is divided into discrete categories for analysis.
• I prefer to keep my personal and work life discrete.
• Let's keep this discrete, okay?
• The artist used discrete brush strokes to create a stunning masterpiece.

noun the act of separating or disconnecting

verb to separate or disconnect

• The committee decided to disjoin the two proposed bills for further discussion.
• Let's disjoin these two topics and focus on one at a time.
• I think it's time to disjoin and move on to something else.
• Sometimes it's necessary to disjoin from toxic relationships for your own well-being.

noun a fact or argument that proves something to be false or incorrect

• The scientist presented solid evidence as a disproof of the previous theory.
• She totally shut down his argument with that disproof.
• He dropped the mic with that disproof!
• Her disproof was like a wrecking ball to his argument.

noun a lack of proportion or equality between two or more things

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• The disproportion between the two groups was evident in the survey results.
• There was a huge disproportion in the number of people at the party.
• The disproportion in their salaries was totally unfair.
• The disproportion in her emotions made it difficult for her to make a rational decision.

adjective Adjectives describe or modify nouns or pronouns. 'Distinct' means recognizably different in nature from something else of a similar type.

adverb Adverbs modify verbs, adjectives, or other adverbs. 'Distinct' can also be used as an adverb to describe how something is done in a recognizably different manner.

• The two species have distinct characteristics that set them apart.
• Each of the twins has a distinct personality.
• Her style is so distinct, she always stands out in a crowd.
• The artist's brush strokes create distinct patterns on the canvas.

noun a distributive number or expression

adjective relating to or serving to distribute or divide among a group or individuals

• The distributive property states that a(b + c) = ab + ac.
• You can use the distributive property to simplify this equation.
• The distributive rule makes math problems easier.
• The distributive nature of leadership allows for shared responsibilities among team members.

noun the act of diverging or moving in different directions

verb to separate and go in different directions

• The two scientific theories began to diverge as new evidence was discovered.
• Our opinions on the movie diverge quite a bit, but that's what makes discussions interesting.
• I can't believe how much our tastes in music diverge - we have nothing in common!
• Their paths in life started to diverge, leading them in different directions.

adjective deviating from a straight line or course

• The two scientific theories are divergent in their conclusions.
• Their opinions on the matter are totally divergent.
• Their ideas are like, totally divergent, dude.
• The paths they chose in life were divergent, leading them in opposite directions.

noun a distinct subset of the Internet with addresses sharing a common suffix

• The company specializes in the financial domain, offering services such as investment management and wealth planning.
• I'm really into the tech domain, always keeping up with the latest gadgets and software.
• She's the queen of the fashion domain, always ahead of the trends and setting new styles.
• His knowledge in the domain of psychology is vast, making him a go-to resource for understanding human behavior.

noun a grammatical number category referring to two items or units

adjective relating to or composed of two parts

• The research study focused on the dual nature of human behavior.
• She enjoys using her dual monitors for work.
• I'm loving the dual exhaust on my new car.
• His dual personality makes it hard to know which side of him will show up.

noun a component or constituent of a whole or one of the parts into which a whole may be resolved

• The periodic table organizes the elements based on their atomic number.
• I love learning about the different elements in chemistry class.
• This new phone has all the cool elements I need for gaming.
• Trust is a key element in any successful relationship.

noun a former measure of length for cloth, equal to 45 inches

verb to move in a twisting or zigzagging course

• The ellipsis is used to indicate the omission of words in a sentence.
• I'll meet you at the ell by the park.
• She's really good at shooting hoops at the ell.
• The ell of uncertainty hung over the outcome of the election.

noun a grammatical structure that is elliptical

adjective relating to or having the form of an ellipse

• The mathematician explained the concept of elliptic curves in great detail.
• I still don't quite understand what those elliptic shapes are all about.
• Elliptic curves are like the cool kids of the math world.
• Her thoughts followed an elliptic path, never quite reaching a clear conclusion.

noun a piece of exercise equipment, typically a stationary machine, used for walking or running in place

adjective relating to or having the shape of an ellipse

• The mathematician explained the concept of an elliptical orbit using precise calculations.
• I prefer using the elliptical machine at the gym instead of the treadmill.
• Let's hit the elliptical for a quick workout sesh.
• Her speech was elliptical, leaving the audience to interpret her true intentions.

verb to mention a number of things one by one in a list

• The report will enumerate all the issues that need to be addressed.
• Can you enumerate all the reasons why you're upset?
• I can't even begin to enumerate the number of times I've been let down.
• Her artwork seemed to enumerate the emotions she couldn't put into words.

adjective calm and even-tempered; not easily disturbed or angered

• His equable temperament allowed him to remain calm in any situation.
• She has always been an equable person, never getting too worked up about anything.
• I wish I could be as equable as him, always keeping my cool.
• The equable flow of the river symbolized the steady rhythm of life.

noun a person or thing that is the same as another in status, value, quality, etc.

verb to be the same as in number or amount

adjective being the same in quantity, size, degree, or value

• In a democratic society, all individuals are considered equal under the law.
• We all have an equal chance of winning the game if we work together.
• No way, we're all equal in the eyes of the boss.
• The two siblings may not look alike, but their love for each other is equal.

verb to consider or treat as equal or equivalent

• It is important not to equate correlation with causation in scientific research.
• Don't equate being busy with being productive.
• Just because you have a lot of followers doesn't equate to being popular.
• She equated his love for her with the warmth of the sun on a summer day.

noun a statement that the values of two mathematical expressions are equal (indicated by the sign =)

• The mathematician solved the complex equation using advanced algorithms.
• I struggled with the equation, but eventually figured it out.
• I totally aced that equation on the test.
• Finding a solution to the problem felt like solving a difficult equation.

noun the state of being equal in value, amount, function, or meaning

• In mathematics, equivalence is a relation that is symmetric, reflexive, and transitive.
• The equivalence between the two theories was undeniable.
• Their friendship reached a level of equivalence where they could finish each other's sentences.
• The artist aimed to create an equivalence between light and darkness in her painting.

adjective Erroneous is an adjective that describes something that is incorrect or mistaken.

• The report contained numerous erroneous data points that needed to be corrected.
• She gave me some erroneous information about the event.
• Don't listen to him, he's always spreading erroneous rumors.
• His belief in the conspiracy theory was based on erroneous assumptions.

noun the quality of being equal in size, shape, or value; uniformity

• The evenness of the distribution of resources among the population is a key factor in achieving social equality.
• I appreciate the evenness of your handwriting, it's very neat and easy to read.
• I can't believe the evenness of her tan, she must have spent hours in the sun.
• The evenness of his temperament is what makes him such a reliable friend in times of need.

verb a word used to describe an action, state, or occurrence

adjective a word or phrase naming an attribute, added to or grammatically related to a noun to modify or describe it

• Please provide the exact measurements for the project.
• Can you tell me the exact time of the meeting?
• I need the exact deets on what happened last night.
• She hit the target with exact precision.

noun the quality of being accurate, precise, or correct

• The scientist emphasized the importance of measuring with exactness in order to obtain accurate results.
• Make sure you follow the recipe with exactness if you want the dish to turn out right.
• She nailed the dance routine with such exactness, it was like she was born to perform.
• His attention to detail and exactness in his work set him apart from his colleagues.

verb a word used to describe an action, state, or occurrence

preposition a word governing, and usually preceding, a noun or pronoun and expressing a relation to another word or element in the clause

• The company decided to offer a discount on all products, excluding the latest model.
• We can go to any restaurant for dinner, excluding the one on Main Street.
• I'm inviting everyone to the party, excluding that one guy who always causes drama.
• She welcomed everyone into her home with open arms, excluding any negative energy.

noun a mathematical expression involving an exponent, a very rapid increase

adjective relating to or using exponentiation, growing at an increasingly rapid rate

• The population growth in urban areas is experiencing exponential growth.
• The number of people moving to the city is growing like crazy.
• The city's population is blowing up!
• The city's growth is like a snowball rolling down a hill, getting bigger and bigger exponentially.

noun a word or phrase that represents an idea or feeling

verb action word that expresses a state of being or an action

adjective describing word that modifies a noun or pronoun

• The artist's painting was a beautiful expression of her emotions.
• I love your expression in that selfie, you look so happy!
• His dance moves are an awesome expression of his style.
• The stormy weather was an expression of nature's power.

noun a circumstance, fact, or influence that contributes to a result or outcome

verb to include or consider as a contributing element

• One significant factor to consider in the decision-making process is the financial aspect.
• A major factor in choosing a college is how close it is to home.
• The main factor for me when picking a restaurant is if they have good fries.
• Trust is a key factor in maintaining a strong relationship with others.

noun a symbol or number used in mathematics or counting

verb to calculate or estimate a number or amount

• The mathematician is a brilliant figurer who can solve complex equations effortlessly.
• She's a great figurer when it comes to planning parties and events.
• I'm not much of a figurer when it comes to budgeting my money.
• He is a key figurer in the company, always coming up with innovative ideas.

adjective having limits or bounds; not infinite; measurable

• The resources available for this project are finite and must be managed carefully.
• We only have a finite amount of time to finish this assignment, so let's get started.
• My patience is finite, so don't push me too far.
• His love for her seemed infinite, but in reality, it was finite like everything else.

adjective an adjective is a word that describes or modifies a noun or pronoun. In this case, 'fixed' is describing something that is repaired or set in place.

• The technician successfully fixed the broken computer.
• I finally fixed my car after it broke down last week.
• I'll have that leak fixed in no time.
• She fixed her gaze on the horizon, lost in thought.

noun the title of a book by Edwin A. Abbott, published in 1884, that satirizes the social hierarchy and rigid thinking of Victorian England through a story about a two-dimensional world called Flatland

• The region is characterized by vast flatland with few hills or mountains.
• I love driving through flatland because you can see for miles.
• Let's go hang out in the flatland and watch the sunset.
• In the flatland of corporate bureaucracy, it can be hard to stand out.

noun a group or community of people who share a common interest or profession

verb to bend something over on itself

• She carefully folded the letter before placing it in the envelope.
• I always fold my clothes before putting them away in the drawer.
• Hey, can you fold this paper airplane for me?
• Under pressure, he finally decided to fold and accept the terms of the negotiation.

noun a particular way in which a thing exists or appears; shape, arrangement, or structure

verb to give shape or visible structure to; to make or fashion into a certain form

adjective pertaining to the form or structure of a thing

preposition used to indicate the structure or arrangement of something

conjunction used to connect different forms or ideas

• The students were required to fill out a registration form for the upcoming conference.
• Hey, can you help me with this form for the school trip?
• I totally aced that test, I'm in top form!
• The team's defense was in solid form during the championship game.

noun a method or procedure for achieving something

• The scientist derived a new formula to calculate the rate of chemical reaction.
• I found this cool formula online that helps solve math problems quickly.
• Dude, I've got the perfect formula for acing that test.
• There's no one-size-fits-all formula for success, you have to find what works for you.

noun a number equal to four times twenty; eighty.

adjective denoting a number four times twenty; eighty.

• Abraham Lincoln famously began his Gettysburg Address with the words 'Fourscore and seven years ago.'
• My great-grandmother lived to be fourscore years old.
• I can't believe he's still kicking at fourscore!
• The company's success was a result of fourscore years of hard work and dedication.

preposition a word that shows the relationship between a noun or pronoun and other words in a sentence, indicating location, direction, or time

• The data was collected from various sources for analysis.
• I heard from Sarah that the party is canceled.
• I got this shirt from the thrift store for a steal.
• The inspiration for her artwork comes from her travels around the world.

noun A thing that plays a central or essential role in an activity, event, or situation

• The fulcrum of the lever is the point where it pivots.
• Make sure the fulcrum is in the right position before lifting the heavy object.
• I can't move this thing without adjusting the fulcrum.
• In this debate, the fulcrum of the argument is the ethical implications of the decision.

noun A complete or whole cycle or series that has returned to its starting point.

adjective Complete or whole; not lacking or missing anything.

• After years of hard work and dedication, her career in journalism has come full circle as she now leads the editorial team.
• It's crazy how things have come full circle - we're back at the same coffee shop where we first met!
• I can't believe we ran into each other again, it's like we've come full circle!
• The family reunion brought everything full circle, reminding us of our roots and where we come from.

noun A break or opening in a barrier or structure

verb There are no applicable verbs for the word 'gap'

adjective There are no applicable adjectives for the word 'gap'

adverb There are no applicable adverbs for the word 'gap'

pronoun There are no applicable pronouns for the word 'gap'

preposition There are no applicable prepositions for the word 'gap'

conjunction There are no applicable conjunctions for the word 'gap'

interjection There are no applicable interjections for the word 'gap'

article There are no applicable articles for the word 'gap'

• There is a significant gap in the data that needs to be addressed.
• We need to fill in the gap in our knowledge about this topic.
• I can't believe there's such a big gap in your story.
• The generation gap between us is evident in our taste in music.

verb to make a general statement or form a general opinion based on limited information

• It is important not to generalize based on limited data in scientific research.
• Don't just assume things about people, you can't generalize like that.
• You can't just lump everyone together, that's not fair to generalize.
• She tends to generalize a lot, seeing patterns where there are none.

verb a word that expresses an action, occurrence, or state of being

• Given the current economic climate, it is important for businesses to adapt and innovate.
• Hey, given that it's raining outside, we should probably bring an umbrella.
• Dude, given how late we are, we better hurry up!
• Given the circumstances, she decided to take a different approach to the problem.

noun a very large number, specifically 10 raised to the power of 100

• A googol is a large number equal to 10 raised to the power of 100.
• I heard that there's a number called googol that's really big.
• Dude, have you ever heard of a googol? It's like a crazy huge number.
• Her love for him was like a googol, immeasurable and infinite.

noun a diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.

• The data was presented in a clear and concise graph during the conference.
• I'll need to see a graph of the numbers before I can make a decision.
• Check out this sick graph showing our progress over time!
• She used a graph to illustrate the ups and downs of her emotional journey.

noun does not apply

verb does not apply

adjective comparative form of the adjective 'great', used to compare two or more things

adverb does not apply

pronoun does not apply

preposition does not apply

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interjection does not apply

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• The company aims to achieve greater market share through strategic partnerships.
• I think we should go for the greater option, it's worth the investment.
• Dude, that new phone is way greater than the one you have.
• With every challenge comes the opportunity for greater growth and learning.

noun a collection or gathering of people or things

verb not applicable

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• The grouping of students was based on their academic performance.
• We're thinking of grouping together for the project.
• Let's do a group-up for the party this weekend.
• The grouping of colors in the painting created a harmonious effect.

noun the act of dividing something into two equal parts

verb the action of dividing something into two equal parts

• The company announced a halving of its workforce in order to cut costs.
• I heard they're halving the prices at the store next week.
• We're halving the workload for the project so it's more manageable.
• The artist's halving of colors in the painting created a striking visual effect.

adjective comparative form of high, used to describe something that is located above or at a greater distance

adverb used to modify a verb, adjective, or other adverb to indicate a higher degree or level

• The company aims to achieve higher profits this quarter.
• I always aim for higher scores on my exams.
• I'm trying to level up and reach higher in my career.
• His aspirations are reaching higher than the stars.

noun a homogeneous substance or mixture

adjective of the same kind or nature; uniform throughout

• The experiment yielded a homogeneous mixture of chemicals.
• All the ingredients in the soup were evenly mixed, making it homogeneous.
• The group of friends was so close-knit, they were like a homogeneous unit.
• The artist aimed to create a painting with a homogeneous color palette to evoke a sense of harmony.

verb to bend or arch one's back into a hump shape

• The camel humped its way across the desert.
• I humped my backpack up the mountain trail.
• He humped his way through the crowded party to get to the bar.
• The project humped along slowly due to unforeseen complications.

noun a cardinal number ten times ten; a unit of 100

adjective being ten times ten

• The company plans to hire a hundred new employees by the end of the year.
• I must have asked her a hundred times to stop texting during the meeting.
• I've seen that movie like a hundred times, it never gets old.
• His generosity knows no bounds, he would give you the shirt off his back a hundred times over.

noun a symmetrical open curve formed by the intersection of a cone with a plane parallel to its side

• The hyperbola is a type of conic section that has two branches, each extending to infinity.
• I learned about hyperbolas in my math class, they're like two sideways U shapes.
• That hyperbola graph is so extra, it looks like a pair of stretched out headphones.
• Her emotions were like a hyperbola, constantly fluctuating between extremes.

noun a person or thing that is not real or does not exist

adjective relating to or existing only in the imagination; not real

• The scientist proposed a theory involving imaginary numbers to explain the phenomenon.
• She likes to daydream about all sorts of imaginary scenarios.
• I can't believe you fell for his imaginary story!
• Her imaginary walls kept her from forming meaningful relationships.

adjective not exact or accurate

adverb in an imprecise manner

• The scientist warned that the data collected from the experiment may be imprecise due to measurement errors.
• I think the directions to the party were a bit imprecise, we got lost a few times.
• The map app on my phone is so imprecise, it always leads me the wrong way.
• Her memory of the event was imprecise, like trying to recall a dream that fades upon waking.

noun a quantity or quality that is too large or too small to be measured or compared

adjective not able to be judged by the same standard as something else; not comparable

• The differences in their opinions were incommensurable, making it difficult to find a common ground.
• Their tastes in music are just incommensurable, they can never agree on what to listen to.
• Their styles are incommensurable, they just don't vibe together.
• The distance between them felt incommensurable, like they were worlds apart.

noun a value that is not able to be measured or compared accurately

adjective not proportionate; inadequate or insufficient

• The measurements of the two objects were incommensurate, making it difficult to compare them accurately.
• Their salaries were incommensurate with the amount of work they were expected to do.
• The prices at that store are totally incommensurate with the quality of their products.
• The distance between them seemed incommensurate with the closeness of their relationship.

noun a small increase or addition

verb to increase or add in small increments

• The company decided to implement a salary increment for all employees.
• I heard there's going to be a small increment in our pay next month.
• My boss promised me a fat increment if I hit my sales target.
• The artist's skill showed a noticeable increment with each painting.

noun a pronoun or other linguistic element that does not specify the identity of its referent

adjective not clearly defined or determined; vague or uncertain

• The contract includes an indefinite clause regarding termination.
• I have an indefinite amount of time to finish this project.
• I'm on indefinite vacation until further notice.
• His love for her was indefinite, never-ending.

adjective not exactly known, determined, or established

• The results of the experiment were deemed indeterminate due to conflicting data.
• I'm not sure about the answer, it's kind of indeterminate.
• The whole situation is so up in the air, it's totally indeterminate.
• Her emotions were in an indeterminate state, fluctuating between joy and sadness.

noun a person or thing that cannot be divided or separated

adjective unable to be divided or separated

• The concept of human rights is based on the belief that they are indivisible and inalienable.
• Our friendship is indivisible, no matter what challenges come our way.
• Me and my bestie are like, totally indivisible - we're like two peas in a pod.
• The bond between mother and child is often described as an indivisible connection that transcends time and space.

adjective limitless or endless in space, extent, or size; impossible to measure or calculate

• The concept of infinity is often studied in mathematics and philosophy.
• I could stare at the stars for an infinite amount of time.
• I swear, that party felt like it went on for an infinite number of hours.
• Her love for him was like an infinite ocean, vast and unending.

adverb in a limitless or endless manner

• The possibilities of artificial intelligence are infinitely vast.
• I could scroll through Instagram infinitely.
• I am infinitely grateful for your help.
• His love for her was infinitely deep.

noun a quantity or value that is extremely small or close to zero

adjective exceedingly small; minute

• The scientist explained that the difference in size was infinitesimal, almost impossible to detect.
• I could barely see the infinitesimal bug crawling on the leaf.
• The chances of winning the lottery are infinitesimal, don't get your hopes up.
• Her patience was wearing thin, reduced to an infinitesimal amount after waiting for hours.

noun a concept describing something that is limitless or endless in space, time, or quantity

• The concept of infinity has intrigued mathematicians and philosophers for centuries.
• I could stare at the stars for infinity and never get bored.
• I'm in love with that new song, I could listen to it for infinity!
• Her kindness seemed to stretch to infinity, always willing to help others.

adjective too many to be counted; countless

• The scientist discovered innumerable new species during his expedition in the rainforest.
• There are innumerable things to do in this city, you'll never be bored.
• I've got innumerable chores to do before my parents get home.
• Her love for him was like an innumerable ocean, vast and endless.

noun a whole or entire unit

adjective necessary for completeness; essential

• Understanding the integral components of this complex system is crucial for its successful operation.
• Being a team player is integral to succeeding in this company.
• Dude, having good vibes is integral to having a great time at the party.
• Patience is integral in building strong relationships with others.

verb to exchange or switch things with each other

• In the experiment, the variables were interchanged to observe any impact on the results.
• We interchanged our seats in the classroom to sit next to our friends.
• I interchanged my shoes with my friend for the party last night.
• The roles of hero and villain were interchanged in the movie, creating a unique storyline.

noun an instance of this, especially in a text or document

• The scientist used interpolation to estimate the missing data points in the experiment.
• I had to do some interpolation to fill in the gaps in my math homework.
• The DJ did some sick interpolation to mix the songs seamlessly.
• His storytelling was so vivid that it felt like he was using interpolation to fill in the details.

verb to insert or introduce (something) between other things or parts; to estimate a value of a function between two known values

• The scientist used advanced mathematical techniques to interpolate missing data points in the research study.
• I had to guess and interpolate the missing information in the report.
• I had to kinda fill in the blanks and interpolate some stuff for the presentation.
• Sometimes in life, we have to interpolate our way through uncertain situations to find the right path.

noun a point or line where two things intersect

verb to cross or meet at a point; to intersect two lines

• The two lines intersect at a single point on the graph.
• The roads intersect just up ahead, so we need to turn left.
• Our interests totally intersect, we should hang out more often.
• The themes of love and loss intersect in this beautiful poem.

noun A point or place where two or more things intersect, especially a road junction.

• The traffic lights at the intersection turned red, signaling all vehicles to stop.
• Hey, let's meet at the intersection near the park later.
• I almost got T-boned at that crazy intersection downtown.
• The intersection of art and technology is where creativity truly thrives.

noun something that is constant or unchanging

adjective not changing or capable of being changed; constant

• The laws of physics are invariable and do not change under different conditions.
• Her love for chocolate is invariable, she can never resist a piece.
• My dad's rule about cleaning your room is invariable - no excuses!
• His commitment to his goals is invariable, like a steady flame that never flickers.

noun a mathematical operation that undoes the effect of another operation

adjective opposite or contrary in position, direction, order, or effect

• The inverse relationship between supply and demand is a fundamental concept in economics.
• In math, the inverse of a function is basically the opposite.
• Dude, it's like the total inverse of what she said last week.
• His actions had the inverse effect of what he intended, causing more harm than good.

verb to put upside down or in the opposite position, order, or arrangement

• The scientist used a special lens to invert the image in the microscope.
• Can you invert the colors on this photo before posting it online?
• I accidentally hit the invert button on my phone and now everything looks weird.
• Sometimes it's necessary to invert our perspective in order to see things more clearly.

noun a very small amount; a tiny bit

• There is not a single iota of evidence to support the claim.
• I don't have an iota of interest in that topic.
• I couldn't care less, not an iota.
• She didn't show an iota of emotion during the entire movie.

noun a person who is not logical or reasonable

adjective not logical or reasonable

• His fear of flying was completely irrational, as statistics show it is one of the safest modes of transportation.
• Irrational fears can really hold you back from trying new things.
• Stop being so irrational, dude. There's no need to freak out over a little spider.
• Her irrational decision to quit her job without having another one lined up left her in a difficult situation.

noun a mathematical or philosophical concept that cannot be broken down further

adjective not able to be reduced or simplified

• The mathematical equation is irreducible and cannot be simplified any further.
• Her love for him was irreducible, no matter what anyone said.
• His stubbornness is irreducible, he never listens to anyone.
• The bond between the two friends was irreducible, nothing could break it.

adjective having rough, sharp points protruding irregularly; uneven or serrated in outline or form

• The hiker carefully navigated the jagged rocks along the cliff.
• Watch out for those jagged edges, they can be sharp!
• I accidentally tripped on that jagged pavement and scraped my knee.
• His words cut through her like jagged knives, leaving emotional wounds.

noun a reason, fact, circumstance, or explanation that justifies or defends

verb to show or prove to be right or reasonable

adjective having a valid reason or explanation

• It is important to justify your reasoning with concrete evidence.
• Can you justify why you need to leave work early?
• I gotta justify my purchase of these new sneakers to my parents.
• Sometimes it's hard to justify our actions in hindsight.

noun the central or most important part of something

• The kernel of the issue lies in the lack of communication between departments.
• The kernel of the problem is that nobody knows how to fix it.
• I heard that new rapper's lyrics are straight fire, he really knows how to drop some kernel.
• The kernel of wisdom in his words resonated deeply with the audience.

noun a structure consisting of strips of wood or metal crossed and fastened together with square or diamond-shaped gaps left between, used as a screen or fence or as a support for climbing plants

• The lattice structure of the crystal was carefully examined under the electron microscope.
• I love sitting under the lattice on the patio during the summer.
• Check out the lattice on that fence, it's so cool!
• The lattice of relationships within the company's hierarchy can be complex to navigate.

adjective smallest in size, amount, degree, etc.

adverb used to indicate the smallest amount or degree

• It is important to consider all possible options and choose the one that will cause the least amount of harm.
• I always try to pick the option that will cost me the least amount of money.
• I'll go with the one that will be the cheapest, at least that way I won't be broke.
• Out of all the paths I could take, I chose the one that seemed to offer the least resistance.

noun the side or direction opposite to the right

verb past tense of leave, to go away from a place or person

adjective located on or relating to the side of the body which is to the west when one is facing north

• He left the meeting early to attend another appointment.
• She left the party before it got too late.
• I can't believe he just left us hanging like that.
• After the accident, she felt like a part of her had left with him.

verb to be in or assume a horizontal or resting position on a surface

adverb in a horizontal or resting position on a surface

preposition used to indicate the location or position of someone or something

• The patient needs to lie on the examination table for the doctor to perform the check-up.
• Just lie on the couch and relax for a bit.
• Let's go lie on the grass and enjoy the sunshine.
• Sometimes it's easier to lie on the problem rather than face it head-on.

noun a point or level beyond which something does not or may not extend or pass

verb to set or serve as a limit to

• There is a strict limit on the number of attendees for the conference.
• I think there's a limit on how many people can enter the building at once.
• Dude, there's like a limit on how much pizza you can eat.
• She felt like there was no limit to her potential after receiving the award.

noun a restriction or constraint

verb to restrict or restrain

adjective restricting or restraining

• The limiting factor in our research was the lack of available data.
• She's always so limiting with her rules and restrictions.
• Don't be so limiting, let's have some fun!
• His fear of failure was limiting his potential for growth.

noun a row or connected series of people or things

verb mark or cover with lines

• Please stand in line and wait for your turn to enter the museum.
• Let's get in line for the concert before it gets too crowded.
• I can't believe we cut the line and got to the front of the club!
• The new policy is a fine line between being fair and being too strict.

noun a mathematical term referring to a straight line or a linear equation

adjective describing something that is arranged in a straight line or following a direct course

• The data points on the graph form a linear relationship.
• The line on the graph goes straight up, it's linear.
• The trend line on the chart is totally linear, dude.
• Her thought process was linear, focusing only on one aspect at a time.

noun The part of something that is below or underneath

adjective Comparative form of low, meaning situated not far above the ground, or having a small distance from the top to the bottom

• The lower interest rates have helped stimulate economic growth.
• Can you lower the volume on the TV?
• I need to lower my expectations for this job interview.
• He tried to lower his guard during the difficult conversation.

noun a pipe or chamber branching into several openings

adjective many and various; having many different forms or elements

• The manifold in the car helps regulate the flow of exhaust gases.
• I had to replace the manifold on my old truck because it was leaking.
• The mechanic said the manifold was shot and needed to be replaced.
• The possibilities for success are manifold if you put in the effort.

adjective relating to or involving mathematics

• The mathematical equation was complex and required advanced problem-solving skills.
• I struggle with mathematical concepts, but I'm working on improving my skills.
• Mathematical stuff always gives me a headache, but I manage to get through it.
• In the grand scheme of things, life is like a mathematical puzzle waiting to be solved.

noun the abstract science of number, quantity, and space, either as abstract concepts (pure mathematics) or as applied to other disciplines such as physics and engineering

• The study of mathematics is essential for understanding complex scientific theories.
• I struggle with mathematics, but I'm trying to improve.
• Mathematics is not my cup of tea, but I have to pass this class.
• In the grand scheme of life, mathematics is like solving puzzles to unlock new opportunities.

noun the greatest or highest possible degree

adjective relating to or being a maximum

• The algorithm aims to find the maximal value in the dataset.
• Let's try to get the maximal score on this test.
• I'm going for the maximal level in this game.
• She reached the maximal potential of her creativity.

noun the branch of mathematics that deals with measurement, especially the determination of the area, volume, or length of geometric figures

• Mensuration is the branch of mathematics that deals with the measurement of geometric quantities.
• I have a mensuration test coming up next week, and I need to start studying for it.
• I find mensuration to be quite challenging, but I'm determined to improve my skills in it.
• The mensuration of his success can be seen in the number of awards he has won.

noun a unit of length in the metric system, equal to 100 centimeters or approximately 39.37 inches

verb None

adjective None

adverb None

pronoun None

preposition None

conjunction None

interjection None

article None

• The scientist used a sophisticated meter to measure the energy levels of the experiment.
• Can you pass me the meter so I can check the distance?
• I need to grab my meter to see if this shirt will fit me.
• She has a keen meter for detecting insincerity in others.

noun a system or standard of measurement based on the meter, gram, and liter as units of length, weight, and capacity

adjective relating to or using the metric system of measurement

• The company uses a variety of metrics to measure their performance.
• I'm not sure how to interpret these metrics they keep sending us.
• Dude, did you see the new metric for tracking likes on social media?
• Her success was not based on traditional metrics, but on her ability to connect with people.

adjective An adjective describes or modifies a noun or pronoun. 'Middlemost' describes something that is in the exact center or middle of a group or range.

• The middlemost point of the city is where the new park will be built.
• I always choose the middlemost seat in the movie theater.
• Let's meet at the middlemost spot in the park later.
• She was the middlemost link in the chain of command.

noun the least or smallest amount or quantity possible

• The company has set a minimum requirement for all employees to have a bachelor's degree.
• You need a minimum of five years of experience to apply for that job.
• I can't go out tonight, I'm on a tight budget so I have to spend the minimum.
• She always gives the minimum effort in everything she does.

verb past tense of mix, meaning to combine different elements or qualities

adjective used to describe something that is made up of different elements or qualities

• The results of the experiment were mixed, with some participants showing improvement while others did not.
• I have mixed feelings about going to the party tonight, I'm not sure if I'm in the mood.
• The new movie got mixed reviews, some people loved it and others thought it was terrible.
• Her emotions were like a mixed bag, ranging from happiness to sadness in a matter of minutes.

adjective describing a quality or attribute that is capable of being changed or altered

• The parameters of the experiment are modifiable based on the researcher's needs.
• You can change the settings on the app, they're modifiable.
• Dude, that hairstyle is totally modifiable with some gel.
• The artist viewed the canvas as a modifiable space for endless creativity.

noun a word or phrase that modifies or describes another word or phrase, typically by adding detail or clarifying meaning

adjective describing or specifying a quality or characteristic of a noun

• In linguistics, a modifier is a word, phrase, or clause that limits or adds information to another part of a sentence.
• She used a modifier to emphasize the importance of her point during the presentation.
• The modifier he added to his outfit really made it stand out.
• Her kindness was a powerful modifier in changing his attitude towards the situation.

noun a number that is a multiple of another

adjective denoting or involving more than one

• The research project involved collecting data from multiple sources.
• I have multiple assignments due this week.
• I'm juggling multiple projects at work right now.
• His mind was like a library with multiple shelves of knowledge.

noun a large number of people or things

adjective having many parts or members

• The conference attracted a multitude of experts from various fields.
• There were a multitude of options to choose from at the buffet.
• The concert had a multitude of awesome bands performing.
• Her mind held a multitude of thoughts and ideas at once.

noun the action or process of making something narrower

verb present participle of the verb 'narrow', indicating the ongoing action of making something narrower

• The narrowing of the road caused traffic congestion during rush hour.
• The narrowing of the path made it difficult to walk side by side.
• I had to squeeze through the narrowing gap to get to the other side.
• His narrowing focus on work has affected his personal relationships.

noun a person or thing that does not converge or come together

adjective describing something that does not converge or come together

• The series of equations is nonconvergent, indicating that there is no limit to the values it can reach.
• The calculations are all over the place, it's like they're nonconvergent or something.
• These numbers just don't add up, they're totally nonconvergent.
• Her thoughts were nonconvergent, jumping from one topic to another without any clear direction.

adjective not consistent or regular in shape or pattern; uneven or variable

• The nonuniform distribution of resources among the population led to social unrest.
• The nonuniform sizing of these shoes is really annoying.
• I hate how nonuniform the rules are around here.
• Her emotions were nonuniform, fluctuating between anger and sadness.

noun a mathematical term meaning zero or nothing

• The mathematician calculated that the sum of the series approached nought as the terms got smaller.
• I'm sorry, but your efforts have amounted to nought in this situation.
• She thought she could outsmart him, but in the end, she got nought.
• His heart felt heavy as he realized he meant nought to her.

noun a state of being legally void or invalid

• The court declared the contract nullity due to a breach of terms.
• The agreement was deemed nullity because they didn't follow the rules.
• Their deal turned out to be a total nullity, such a waste of time.
• The artist saw beauty in the nullity of the blank canvas, a potential waiting to be filled.

adjective describing word that modifies a noun or pronoun, in this case, 'numberless' describes a noun as being without a specific number or countless

• The scientist encountered a numberless amount of variables in his research.
• There were numberless options to choose from at the buffet.
• I have a numberless amount of homework to do tonight.
• Her creativity knew no bounds, as she came up with numberless ideas for the project.

noun a mathematical value or figure representing a quantity

verb not applicable

adjective not applicable

adverb not applicable

pronoun not applicable

preposition not applicable

conjunction not applicable

interjection not applicable

article not applicable

• The numbers on the financial report indicate a positive trend in sales.
• Can you check the numbers on the spreadsheet to make sure they add up?
• I'm not good with numbers, so I struggle with math homework.
• In the grand scheme of things, we are just numbers in the population.

adjective describing a noun as capable of being counted or numbered

• The set of prime numbers is numerable and can be listed in order.
• There are a numerable amount of books in the library for you to choose from.
• There are like a numerable options for lunch at the food court.
• The artist's creativity seemed numerable, as they effortlessly produced masterpiece after masterpiece.

verb to count or enumerate

adjective skilled in or relating to basic mathematics

• It is important to be able to numerate accurately in order to make sound financial decisions.
• I need to numerate how much money I have left after paying my bills.
• I can't believe she can't even numerate simple addition.
• The poet's words were so powerful, they seemed to numerate the emotions of the audience.

adjective describing or relating to numbers or numeration

• The numerative system used in ancient civilizations was based on symbols representing different quantities.
• I never understood the numerative system they use in that country, it's so different from ours.
• I can't deal with all these numerative symbols, it's too confusing for me.
• The numerative language of music allows musicians to communicate complex rhythms and melodies.

adjective describing a number or relating to numbers

• The report includes a detailed analysis of the numeric data collected from the survey.
• I need to double-check the numeric values in the spreadsheet before submitting it.
• I'm not great with numbers, so I struggle with numeric calculations sometimes.
• The numeric value of her kindness cannot be measured in mere numbers.

adjective relating to or expressed as a number or numbers

• The research study presented a detailed analysis of the numerical data collected.
• Can you help me with these numerical calculations for my homework?
• I'm not good with all those numbers and numerical stuff.
• His argument was strong, but lacked the numerical evidence to support it.

noun a person or thing to which an action, feeling, or thought is directed

verb to express or feel disapproval, dislike, or distaste for something

adjective not influenced by personal feelings or opinions; unbiased

adverb used to emphasize a following element

preposition used to introduce the complement of a verb

conjunction used to introduce a clause or sentence contrasting with what has already been mentioned

• The scientist used a microscope to observe the tiny object.
• Can you pass me that object over there?
• Check out this cool object I found at the thrift store.
• His love for her was like a precious object that he cherished.

noun a symbol or function representing a specific operation or action

• The telephone operator connected the call to the correct department.
• Can you ask the operator to transfer me to the sales team?
• The operator totally hooked me up with a discount on my bill.
• As the operator of the project, she made sure everything ran smoothly.

noun something that is completely different from something else

adjective contrary or radically different in some respect

• The building on the opposite side of the street is a bank.
• The house opposite ours is painted a bright red.
• I can't stand that guy, he's the opposite of cool.
• Her personality is the complete opposite of her sister's.

adjective describing something that lacks order or organization

• The orderless stack of papers on the desk needs to be organized.
• I can't find anything in this orderless mess!
• Her room is so orderless, it's like a tornado went through it.
• His thoughts were orderless, jumping from one idea to the next without any coherence.

noun a number denoting position in a series, such as first, second, third

adjective relating to or denoting a numerical order

• In mathematics, an ordinal number is used to describe the position or rank of an element in a sequence.
• The ordinal ranking of the students in the class was based on their GPA.
• I'm always last in line, I guess I have the 'ordinal' luck.
• His love for her was not just first or second, but of an ordinal nature that surpassed all others.

verb to kiss or touch with the lips, to come into close contact or union

• The two circles osculate at exactly one point.
• The two circles touch each other at one point.
• The circles are kissing at that one point.
• Their ideas osculate, leading to a collaborative project.

noun a part or portion that extends over or across another

verb to extend over or cover part of

adjective having an area, range, or scope that coincides with or includes part of another

• There is an overlap in the responsibilities of the two departments.
• The schedules overlap, so we can carpool to work together.
• Our interests overlap, so we should hang out sometime.
• The themes of the two books overlap, making for an interesting comparison.

noun a word, phrase, number, or other sequence of characters which reads the same backward as forward

• A palindrome is a word, phrase, number, or other sequence of characters that reads the same forward and backward.
• I love finding palindromes like 'racecar' that read the same forwards and backwards.
• Palindromes are so cool - they're like words that are the same even when you flip them around!
• In life, sometimes things come full circle and feel like a palindrome - starting and ending in the same way.

noun a person or thing that is similar or analogous to another

verb to be parallel to; be similar or analogous to

adjective having the same direction, course, nature, or tendency; corresponding; similar

• The two lines are parallel to each other, never intersecting.
• These two roads run parallel to each other for miles.
• We're like parallel lines - always close but never crossing paths.
• His career path is running parallel to hers, both steadily moving forward.

noun a part or portion of a whole

adjective existing only in part; incomplete

• The research study only provided a partial analysis of the data.
• I only have a partial understanding of the instructions.
• I'm only halfway there, just got a partial grasp on the concept.
• Her partial commitment to the project hindered its progress.

noun a place or position on a scale or in a sequence

verb to fasten or secure with a peg

• She used a peg to hang up the laundry on the clothesline.
• Can you pass me that peg so I can clip this paper together?
• I need to peg this project before the deadline hits.
• His comment really pegged her self-esteem.

noun a boundary that surrounds an area or object

adjective pertaining to the outer boundary of an area or object

• The security guards patrol the perimeter of the building every hour.
• Let's walk around the perimeter of the park before heading home.
• We scoped out the perimeter of the party to see if there was a way to sneak in.
• She kept her emotions tightly guarded, never letting anyone breach the perimeter of her heart.

noun a permutable element or factor

adjective able to be rearranged or reorganized in different ways

• Mathematicians study the properties of permutable elements in abstract algebra.
• You can rearrange the letters in that word to make a permutable word.
• I love how these emojis are permutable, you can mix and match them however you want.
• In literature, the author uses permutable symbols to convey different meanings to the readers.

noun an airplane or similar aircraft

• The plane experienced some turbulence during the flight.
• I always get nervous before getting on a plane.
• Let's catch a plane to Vegas for the weekend!
• Her career is really taking off like a plane.

verb to plan or scheme secretly

adjective having a plot or storyline

• The architect carefully plotted the layout of the new building.
• She plotted out her schedule for the week ahead.
• They plotted to sneak out of the house without their parents knowing.
• The author plotted a thrilling twist in the story that kept readers on the edge of their seats.

noun a word or form that denotes more than one

adjective referring to or involving more than one

• In English grammar, the plural form of 'cat' is 'cats'.
• Most people prefer using the plural form of 'they' instead of 'he' or 'she'.
• I can't believe how many likes my photo got - the plurals are blowing up!
• The plural of happiness is not possessions, but experiences.

noun a card game involving skill and gambling, played with a standard deck of 52 cards

• Many people enjoy playing poker as a form of entertainment and skill.
• Let's gather at my place tonight for some poker games!
• I'm feeling lucky tonight, let's hit up the poker tables.
• Negotiations in politics can sometimes feel like a high-stakes game of poker.

adjective describing or referring to something that comes before or is in front of something else

• The analysis of the data from the preceding year showed a significant increase in sales.
• I can't believe you missed the movie that was on right before the one we watched. It was the preceding film.
• I heard the party at Sarah's house was lit, but I couldn't make it because of the preceding engagement I had.
• The artist carefully studied the strokes in the painting preceding his, trying to learn from the master's technique.

noun a word, letter, or number placed before another

verb to add a prefix to a word or number

• In linguistics, a prefix is an affix which is placed before the stem of a word.
• Make sure to include the correct prefix before the word to form the right meaning.
• I always forget to add the prefix when texting, it's so annoying!
• Adding a positive prefix to your mindset can lead to a more optimistic outlook on life.

noun a state or time of greatest strength, vigor, or success in a person's life

verb prepare (something) for use or action, typically by means of a special process

adjective of the best possible quality; excellent

• The company is focused on delivering prime quality products to its customers.
• I always go to that prime spot for the best burgers in town.
• She's always looking for a prime opportunity to show off her skills.
• In his prime, he was considered the prime example of a successful businessman.

noun an estimate or forecast of a future situation or trend

• The financial analyst presented a detailed projection of the company's revenue for the next quarter.
• The teacher showed us a projection of our grades if we don't start studying more.
• I made a projection that we'll be at the beach by noon.
• His projection of confidence in the meeting was impressive.

noun evidence or argument establishing a fact or the truth of a statement

verb to demonstrate the truth or existence of something by providing evidence or argument

• The scientist presented irrefutable proof of his groundbreaking discovery.
• I need some proof that you actually did your homework.
• She showed me the receipts as proof that she was telling the truth.
• His success in the competition was the ultimate proof of his dedication and hard work.

adjective relating to, based on, or involving proportion

• The amount of tax you pay is directly proportional to your income.
• The more hours you work, the more money you make - it's proportional.
• If you study harder, your grades will go up in a proportional way.
• In relationships, trust should be proportional to loyalty.

adjective having a proper or suitable relationship in size, amount, or degree

adverb in a proportionate manner

• It is important to ensure that the punishment is proportionate to the crime committed.
• The punishment should match the crime, it has to be proportionate.
• The consequences gotta be fair, they need to be proportionate.
• In life, the effort you put in is proportionate to the results you achieve.

noun the state or quality of being provable

adjective capable of being proven or demonstrated

• The mathematical theorem was provable using advanced calculus techniques.
• I can prove it to you, it's totally provable.
• Dude, that theory is so provable, you can't argue with it.
• Her dedication to her craft was provable through the quality of her work.

noun a test or trial to establish the truth or validity of something

verb to demonstrate the truth or existence of something by providing evidence or argument

• The scientist conducted multiple experiments to prove his hypothesis.
• I bet I can prove you wrong about that.
• I'll show you the evidence to prove my point.
• Her actions will prove her loyalty to the team.

verb to demonstrate or establish the truth or accuracy of something

• The research study proved that there is a direct correlation between exercise and mental health.
• She proved everyone wrong by finishing the marathon despite her injury.
• He proved he's got skills on the basketball court.
• Her dedication to the project proved to be the key to its success.

noun an area or region with a particular feature or characteristic

• The research team divided the data into four quadrants for analysis.
• Let's meet at the coffee shop in the northeast quadrant of the mall.
• I heard that party was in the cool quadrant of town.
• She felt like she was in a different quadrant of life after starting her new job.

noun the process of determining or expressing the quantity, amount, or extent of something

• The quantification of the data allowed for a more accurate analysis.
• We need to figure out the quantification of this problem before we can solve it.
• I'm not sure about the quantification of that, it's all a bit fuzzy.
• The quantification of her love for him was immeasurable.

noun a group of atoms behaving as a unit in a number of compounds

adjective relating to or affecting the fundamental nature of something; far-reaching or thorough

• The scientist proposed a radical new theory that challenged existing beliefs.
• She made a radical decision to quit her job and travel the world.
• That new video game is so radical, dude!
• The artist used radical colors and shapes to create a visually striking masterpiece.

noun a Latin word meaning 'root' or 'origin', used in mathematics and computer science to refer to the base number or foundation of a system

• The radix of a number system is the base or foundation upon which it is built.
• The radix is like the starting point for a number system.
• The radix is basically the boss of the number system.
• Just as the radix is the root of a number system, our values serve as the radix of our character.

noun the area of variation between upper and lower limits

verb to extend or stretch across a distance

• The store offers a wide range of products to choose from.
• They have a bunch of different stuff in stock.
• They've got a whole range of things to pick from.
• Her emotions ran the range from joy to sorrow throughout the day.

adverb In a logical and reasonable manner.

• It is important to approach decision-making rationally, considering all the relevant factors.
• Let's think about this rationally before jumping to any conclusions.
• Dude, you gotta chill out and think about this rationally.
• She approached the problem rationally, like a chess player thinking several moves ahead.

noun something that occurs again

• The doctor explained that the patient's symptoms may be due to the recurrence of the underlying condition.
• I heard there might be a recurrence of the issue we had last year.
• I can't believe the recurrence of drama in this group chat.
• The recurrence of bad habits can be detrimental to one's overall well-being.

verb to make or become twice as much or as many

• In order to meet the deadline, we must redouble our efforts.
• We need to really step up our game to get this done on time.
• Let's kick it up a notch and redouble our efforts.
• Sometimes in life, we need to redouble our determination to overcome obstacles.

verb to make smaller or less in amount, degree, or size

adjective made smaller or less in amount, degree, or size

• The company implemented cost-cutting measures which reduced expenses significantly.
• I found a coupon that reduced the price of the shoes I wanted to buy.
• I haggled with the seller and managed to get the price reduced by half.
• Her harsh words reduced him to tears.

noun a decrease or lessening in amount, size, or importance

• The company implemented a cost reduction strategy to improve profitability.
• We're trying to cut costs to save money.
• Let's trim the fat to increase our savings.
• She made a reduction in her social circle to focus on her studies.

noun the quality or state of being regular; conformity to a standard, rule, or pattern

• The regularity of his daily routine helped him stay organized and focused.
• I try to exercise with some regularity, but sometimes life gets in the way.
• I can't believe the regularity of her excuses for being late all the time.
• The regularity of the waves crashing on the shore was like a soothing rhythm.

verb to make regular or consistent

• The government is working to regularize the process for obtaining work permits.
• I need to regularize my sleeping schedule, it's all over the place.
• I gotta regularize my gym routine, I've been slacking off lately.
• She tried to regularize her emotions, but the chaos inside her was too overwhelming.

noun a person who is connected by blood or marriage; a relative

• The company is looking to establish a strong business relation with their new partners.
• I have a good relation with my neighbor, we often help each other out.
• I'm in a complicated relation with my ex, it's hard to move on.
• The relation between hard work and success is undeniable.

adverb relatively is an adverb that is used to describe something in comparison to something else, indicating a moderate or reasonable degree of something

• The company's profits have been relatively stable over the past few quarters.
• I think the new restaurant is relatively good, we should try it out sometime.
• She's relatively chill, you'll get along with her just fine.
• His success in the competition was relatively a walk in the park compared to the challenges he faced before.

noun the act of changing the form or structure of something

verb to change the form or structure of something

• The company plans to reshape its business strategy in order to adapt to changing market conditions.
• I'm thinking about reshaping my garden to make it more visually appealing.
• I need to reshape my workout routine to get better results.
• The unexpected turn of events forced me to reshape my plans for the future.

noun a small amount of something that remains after the main part has gone or been taken or used

verb N/A

adjective N/A

adverb N/A

pronoun N/A

preposition N/A

conjunction N/A

interjection N/A

article N/A

• The residue left behind after the chemical reaction was carefully analyzed in the lab.
• There was some residue from the party last night that we need to clean up.
• I hate it when there's residue on my dishes after I wash them.
• The residue of his past mistakes still lingered in his mind, affecting his decisions.

adjective capable of being resolved or settled; solvable

• The issue at hand is easily resolvable with the right approach.
• Don't worry, this problem is totally resolvable.
• No sweat, we can totally resolve this.
• Like pieces of a puzzle, the situation is resolvable with some effort.

noun a substance that dissolves another substance

adjective having the power to dissolve or resolve something

• The resolvent of the equation helped us find the roots.
• Using the resolvent made solving the problem a lot easier.
• I just plugged in the resolvent and got the answer in no time.
• The resolvent acted as a key to unlocking the solution to the puzzle.

noun Resultant can also be used as a noun to refer to the outcome or consequence of a specific action or event.

adjective Resultant is used as an adjective to describe something that is produced as a result of something else.

• The resultant of the two forces acting on the object can be calculated using vector addition.
• The final outcome is dependent on the resultant of all the factors involved.
• The party was a disaster, but the resultant was that we all had a good laugh about it later.
• Her decision to quit her job had a resultant effect on her mental health.

noun the opposite or contrary of something

verb to move backwards or in the opposite direction

adjective opposite or contrary in position, direction, order, or nature

adverb in a way that is opposite or contrary

• The scientist conducted an experiment to determine if the reaction could be reversed.
• I accidentally reversed the order of the steps in the recipe.
• He tried to reverse out of the parking spot but ended up hitting the car behind him.
• Sometimes in life, we need to take a step back in order to reverse our course and move forward in a better direction.

verb to change something to its opposite or backward position

adjective opposite or contrary in position, direction, order, or effect

• The decision was reversed by the higher court.
• They changed their minds and reversed the decision.
• They totally flipped the script and reversed their decision.
• The tables have turned and the decision has been reversed.

noun a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides

• The rhomboid muscle is located in the upper back and helps with shoulder movement.
• I can feel my rhomboid muscle getting sore from all the heavy lifting.
• I need to work on my rhomboids at the gym to get that V-shape back.
• Her rhomboid personality traits make her stand out from the crowd.

adjective directed or moving toward the right

adverb toward the right

• The car turned rightward at the intersection.
• Go rightward at the next street.
• Hang a rightward up ahead.
• His career took a rightward turn after he switched companies.

noun the part of a plant that attaches it to the ground and gathers water and nutrients

verb to establish deeply and firmly

adjective basic or fundamental

adverb rootedly

• The root of the problem lies in the lack of communication within the team.
• I heard the root cause of the issue was a misunderstanding between them.
• She's always at the root of drama in our friend group.
• His love for music has deep roots in his family's musical heritage.

noun a device for weighing

verb to climb up or over something using both feet and hands in a series of movements

• The scale of the project requires careful planning and coordination.
• The scale of this party is going to be massive!
• I can't believe the scale of that concert last night, it was lit!
• The scale of her ambition knows no bounds.

noun a unit of time equal to one sixtieth of a minute

adjective coming after the first in order or sequence

adverb in the second place; secondly

• The second speaker at the conference discussed the importance of renewable energy.
• Can you wait a second? I just need to grab my phone.
• I'll catch you in a hot second, just finishing up here.
• She was second in command, always ready to step up when needed.

noun a separate person or thing

adjective existing or considered independently

adverb in a separate or distinct manner

• The two experiments were conducted separately to ensure accurate results.
• Let's meet separately to discuss our individual contributions.
• We should chill separately tonight and catch up on our favorite shows.
• Their paths in life diverged, leading them to walk separately towards their dreams.

noun a collection of objects or items that belong together, often used for a specific purpose

verb to put or place something in a particular position or location

adjective fixed or arranged in a particular way

adverb in a fixed or rigid manner

• The committee has set a date for the next meeting.
• I've set aside some time to work on my project this weekend.
• Let's set up a hangout at the park tomorrow.
• She has set her sights on becoming the next CEO of the company.

noun a geometric figure such as a square, circle, or triangle

verb to give a particular form or appearance to; to mold or make

adjective having a particular form or appearance

• The artist carefully studied the shape of the sculpture before beginning to carve.
• I'm trying to get back in shape before summer hits.
• That new car has a sleek shape that really stands out.
• Her words took shape as she began to articulate her thoughts.

noun a person who sharpens things or makes them more acute

adjective describing a person or thing that is more keen or intelligent

• The surgeon used a sharper scalpel to make precise incisions during the operation.
• I need to buy a sharper knife for cutting vegetables in the kitchen.
• Dude, you need to get a sharper haircut before the party.
• Her wit is sharper than a knife, always quick with clever comebacks.

adjective having a resemblance in appearance, character, or quantity without being identical

• The two research studies produced similar results.
• My sister and I have similar taste in music.
• We both have similar vibes, dude.
• Their friendship was like two peas in a pod, always thinking in a similar way.

noun a likeness or resemblance, especially in a way that is used as a basis for comparison

• The similitude between the two research studies is striking.
• I noticed a similitude in their fashion sense.
• Their taste in music has a crazy similitude.
• The similitude of their personalities is like two peas in a pod.

noun a person or thing that is single, unique, or the only one of its kind

adjective relating to or being a singleton

• In software engineering, a singleton is a design pattern that restricts the instantiation of a class to one object.
• Hey, did you know that a singleton is like a special class that can only have one instance?
• Bro, that singleton thing in coding is like having a one-of-a-kind class, you feel me?
• Just like a rare gem, a singleton in programming is a unique and valuable entity.

noun a thin, flat piece of food that has been cut from a larger portion

verb to cut something into thin, flat pieces

• Please cut me a thin slice of the cake.
• Hey, can you pass me a slice of pizza?
• I could really go for a slice of that pie right now.
• She was able to slice through the competition with ease.

noun a surface of which one end or side is at a higher level than another; a rising or falling surface

verb to have or take an inclined or oblique direction or angle

• The slope of the line can be calculated using the rise over run formula.
• Be careful walking on that slope, it's pretty steep.
• I almost wiped out trying to snowboard down that gnarly slope.
• His grades have been on a downward slope since the beginning of the semester.

adjective a word that describes or modifies a noun, such as 'small' describing the size of an object

• The small size of the apartment made it difficult to fit all the furniture.
• I found a small cafe down the street that serves amazing coffee.
• Let's hit up that small burger joint for lunch.
• His influence may seem small, but it has a big impact on the community.

noun the quality or state of being small in size

• The smallness of the apartment made it difficult to fit all of the furniture.
• I love the smallness of this coffee shop, it feels cozy and intimate.
• I can't believe the smallness of that dog, it's so cute!
• The smallness of her heart was evident in the way she treated others.

noun the state of being scarce or in short supply; a small amount or number

• The sparsity of data in this study makes it difficult to draw meaningful conclusions.
• There's a real sparsity of good restaurants in this area.
• I can't believe the sparsity of snacks in this house!
• The sparsity of love in his life left him feeling empty.

noun a person or thing regarded as being exceptional or distinctive

adjective better, greater, or otherwise different from what is usual

• In this particular scenario, we need to consider a special case that requires a different approach.
• Hey, there's a special case we need to look at before making any decisions.
• Yo, this is a special case we gotta handle differently.
• Just like in a deck of cards, the joker is a special case that can change the game.

noun a pile of objects, typically one that is neatly arranged

verb to arrange (a number of things) in a pile, typically a neat one

• The programmer implemented a stack data structure to efficiently manage the data.
• I need to stack up these books before they fall over.
• Let's stack some cash and hit the town tonight.
• The odds were stacked against her, but she persevered and succeeded.

noun a crackling or hissing noise caused by electrical interference

adjective lacking in movement, action, or change

• The static on the television screen was caused by poor reception.
• I can't hear you clearly, there's too much static on the line.
• The static on this radio station is so annoying, I can't even hear the music.
• His mind was filled with static, making it hard for him to focus on his work.

noun a person who is below average in intelligence or development

adjective below the normal or average level

• The psychologist diagnosed the patient with subnormal cognitive abilities.
• Some people may consider his behavior to be subnormal, but I think he's just unique.
• She thinks she's so cool, but really she's just subnormal.
• The team's performance was subnormal compared to their usual standards.

noun the total amount resulting from the addition of two or more numbers

verb to calculate the total of two or more numbers

• The sum of the two numbers is equal to 10.
• What's the sum of these figures?
• I can't believe the sum of our bill was so high!
• The sum of all our efforts finally paid off in the end.

noun a total or summary of items

adjective relating to or constituting a sum

• The summation of all the data points resulted in a clear trend analysis.
• When you add up all the numbers, you get the summation of the data.
• Dude, the whole thing is just the summation of everything we've been talking about.
• The painting was the artist's summation of all his experiences and emotions.

noun the act of supposing or assuming

verb to assume or believe something to be true without definite proof

• Suppose we were to implement a new policy to address this issue.
• Suppose we all pitch in to help out, what do you think?
• Suppose we chill at the park instead of going to the movies.
• Suppose our dreams were made of stardust, how would that change our perspective on life?

noun a surd is a mathematical term referring to a number that cannot be expressed as a ratio of two integers, such as the square root of a non-square number

• The mathematician explained the concept of a surd in great detail during the lecture.
• I still don't understand how to simplify a surd in my math homework.
• I'm so over these surds in algebra class.
• The complexity of the situation was like trying to simplify a surd without knowing the rules.

verb to make symmetrical; to create or establish symmetry

• In order to achieve a balanced design, we need to symmetrize the elements on both sides.
• Let's symmetrize the photos on the wall so it looks more organized.
• I'm going to symmetrize my outfit by adding a matching hat.
• The artist sought to symmetrize the chaos of the cityscape in his painting.

noun the quality of being made up of exactly similar parts facing each other or around an axis

• The scientist studied the symmetry of the crystal structure.
• The artist loves using symmetry in her paintings.
• Dude, that skateboard trick had perfect symmetry!
• There is a beautiful symmetry in the way the seasons change.

adjective relating to or along a tangent; diverging from a previous course or line; only slightly connected; digressive

• The speaker often went off on tangential points during the presentation, making it difficult to follow the main argument.
• I know I went off on a tangential rant during our conversation, but I just had to get it off my chest.
• She always goes off on these tangential tangents that have nothing to do with what we're talking about.
• His thoughts were like a web of tangential connections, leading us further and further away from the original topic.

verb Tangled is also used as a verb to indicate the action of becoming twisted together or caught in a snarl.

adjective Tangled is used as an adjective to describe something that is twisted together in a confused mass.

• The vines in the forest were so tangled that it was difficult to walk through.
• I tried to untangle the tangled mess of wires behind the TV.
• Her hair was so tangled after the windstorm, it took hours to brush out.
• The web of lies he had spun became more tangled with each new fabrication.

noun a word or phrase used to describe a thing or to express a concept, especially in a particular kind of language or branch of study

verb to give a descriptive name to; call by a specified term

adjective relating to or denoting a specified period of time or a particular condition or state of affairs

preposition used to specify a particular time, period, or condition

article a word that is used with a noun to specify grammatical definiteness of the noun, and in some languages extending to volume or numerical scope

• In academic circles, the term 'anthropology' refers to the study of human societies and cultures.
• I'll need to look up the meaning of that term before I can fully understand the article.
• I'm not familiar with the slang term 'lit' - what does it mean?
• The term 'butterflies in my stomach' is often used figuratively to describe nervousness or excitement.

verb to form or arrange small squares or blocks in a checkered or mosaic pattern

• The tiles on the floor tessellate perfectly, creating a seamless pattern.
• I love how the tiles tessellate in the bathroom, it looks really cool.
• Check out how these tiles tessellate, it's so satisfying to look at.
• The different elements of the design tessellate together to create a harmonious whole.

adverb at that time; at the time in question

conjunction used to introduce a logical conclusion or sequence of events

• First, gather all the necessary materials, then proceed to follow the instructions carefully.
• Let's grab some lunch, then we can decide what to do next.
• I aced my exam, then I treated myself to some ice cream.
• She took a leap of faith, then watched as her dreams began to unfold.

noun a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths

• The theorem states that the sum of the angles in a triangle is always 180 degrees.
• Hey, did you hear about that math theorem that proves triangles always have angles that add up to 180 degrees?
• Yo, check out this crazy math theorem that shows how triangle angles always add up to 180 degrees!
• Just like the theorem of cause and effect, every action has a consequence.

adverb used to introduce a logical conclusion or consequence

conjunction used to introduce a logical conclusion or consequence

• The experiment yielded significant results; therefore, further research is warranted.
• I studied hard for the test and aced it, so I'm treating myself to ice cream.
• I saved up enough money, so I'm gonna splurge on some new kicks.
• She planted the seeds with care and watered them diligently; therefore, a beautiful garden bloomed in her backyard.

noun a person or animal that is thin

adjective having little thickness or depth; not dense or crowded

• The scientist used a thin layer of coating to protect the delicate material.
• She always wears those thin leggings to the gym.
• I'm trying to slim down and get thin for summer.
• The line between love and hate is very thin.

noun a covering made of tiles

verb present participle of tile, which means to cover with tiles

• The tiling in the bathroom was expertly done, with each tile perfectly aligned.
• I'm thinking of redoing the tiling in my kitchen to give it a fresh look.
• I watched a DIY video on YouTube and now I'm ready to tackle the tiling in my shower.
• The tiling of the puzzle pieces was a satisfying challenge to complete.

adjective easily managed or controlled; docile

• The problem was quite tractable once we broke it down into smaller components.
• Don't worry, this issue is actually pretty tractable and we can easily solve it.
• This math homework is totally tractable, we got this!
• Her emotions were like a wild horse, but with time and patience, they became more tractable.

adjective relating to a spiritual or non-material realm; beyond ordinary experience

• The philosopher discussed the concept of transcendental knowledge in his latest book.
• I don't really understand all that transcendental stuff the professor was talking about.
• Transcendental ideas can be pretty out there, man.
• Her artwork was described as having a transcendental quality that touched the soul.

noun a thorough or dramatic change in form or appearance

verb None

adjective None

adverb None

pronoun None

preposition None

conjunction None

interjection None

article None

• The company underwent a significant transformation after implementing new technology.
• She's had a complete transformation since starting her new job.
• His style transformation is on point - he's really upped his game.
• The caterpillar's transformation into a butterfly is a beautiful metaphor for growth and change.

noun a mathematical operation in which the positions of elements in a matrix are switched

verb to change the position or order of something

• In mathematics, to transpose a matrix means to switch its rows with its columns.
• Can you transpose these two numbers for me?
• Let's just transpose the order of these events to make it easier.
• She tried to transpose her feelings of anger into feelings of forgiveness.

verb to change the position or order of something

adjective having changed the position or order of something

• The melody was transposed to a lower key for the soprano singer.
• I transposed the numbers in the spreadsheet to make them easier to read.
• I totally transposed my plans and ended up at the wrong party.
• Her emotions were transposed from sadness to joy after receiving the good news.

noun a trigonometry, a branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles

adjective neat and trim in form or appearance

• The trigonometry problem required students to solve for the missing angle.
• I struggled with the trig question on the math test.
• I aced that trig problem like a boss.
• She had a trig approach to solving complex issues, breaking them down into smaller parts.

noun a branch of mathematics that deals with the relationships between the sides and angles of triangles, especially right triangles

• Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
• I struggled with trigonometry in high school, but eventually got the hang of it.
• Trig can be a real pain sometimes, but it's not too bad once you understand it.
• Navigating through life's challenges is like solving a complex trigonometry problem, requiring careful calculation and precision.

noun a number that is three times as large as another

verb to make three times as large or as numerous

adjective consisting of three parts or things

• The company reported a triple increase in profits this quarter.
• I scored a triple in the bowling game last night!
• She's always triple checking everything before submitting it.
• His betrayal felt like a triple stab in the back.

noun a thing that is of little value or importance

adjective relating to or characteristic of being trivial

• The professor emphasized the importance of focusing on the main points of the research and avoiding triviality.
• Stop worrying about the triviality of the situation and focus on what really matters.
• Don't sweat the small stuff, it's just triviality.
• In the grand scheme of things, the triviality of the argument seemed insignificant.

noun a low point in a business cycle

• The farmer filled the trough with feed for the livestock.
• Make sure to fill up the trough before the animals get hungry.
• I found some coins in the trough at the fountain.
• She hit a trough in her career but eventually bounced back stronger.

verb to shorten something by cutting off a part of it

adjective describes a word or phrase that has been shortened or cut off

• The data set was truncated to remove any outliers before analysis.
• I had to cut the article short and truncated some parts to fit the word limit.
• I quickly truncated my message to just a few words to send it before the meeting started.
• His dreams were truncated by the harsh reality of life.

noun a surface or object that has two opposite sides

adjective describing a surface or object that has two opposite sides

• The contract was written in a two sided format to clearly outline the responsibilities of both parties.
• The pamphlet is two sided, so make sure to read both sides for all the information.
• I like to keep my options open and see things from a two sided perspective.
• Her decision was two sided, weighing the pros and cons before making a choice.

adjective not limited or restricted in any way; infinite

adverb in an unbounded manner; without limits or restrictions

• The potential for growth in the new market is unbounded.
• Her creativity is unbounded; she always comes up with new ideas.
• His energy is unbounded, he never seems to run out of steam.
• The artist's imagination was unbounded, leading to unique and captivating works of art.

adjective describing something that has not been planned or thought out in advance

• The uncalculated risks taken by the company led to a significant financial loss.
• His uncalculated decision to quit his job without another one lined up was risky.
• She made an uncalculated move in the game that cost her the win.
• His uncalculated words during the argument caused irreparable damage to their relationship.

adjective describing a state or condition that does not change or vary

• The laws of physics are unchanging and constant throughout the universe.
• My grandmother's routine is unchanging, she does the same thing every day.
• His style is so unchanging, he needs to switch it up sometimes.
• The unchanging nature of the mountain symbolizes stability and endurance.

adjective describing a quality of being constant or unchanging

• Her undeviating commitment to the company's values earned her a promotion.
• He has an undeviating love for chocolate chip cookies.
• I admire your undeviating dedication to binge-watching TV shows.
• The undeviating path to success is paved with hard work and determination.

adjective an adjective describes or modifies a noun or pronoun, in this case 'undiscoverable' describes something that cannot be discovered

• The undiscoverable truth about the ancient civilization remains a mystery to this day.
• The undiscoverable treasure is rumored to be hidden somewhere in the old abandoned mansion.
• I heard there's some undiscoverable stuff at the bottom of the lake, wanna go check it out?
• Her true feelings were like an undiscoverable treasure buried deep within her heart.

adjective complete or total

• The company's undivided attention to customer service has led to increased satisfaction rates.
• I appreciate your undivided support in helping me with this project.
• I need your undivided focus on this game, no distractions!
• His undivided loyalty to the team was unwavering, even in the face of adversity.

adverb modifies a verb, adjective, or another adverb by providing information on how the action is performed or how something is described

• The paint was applied unevenly, resulting in a streaky finish.
• She cut the cake unevenly, but it still tasted delicious.
• The basketball court was paved so unevenly, it was like playing on a rollercoaster.
• Her emotions were distributed unevenly, with moments of extreme joy followed by deep sadness.

verb to open or spread out from a folded position

• The events of the meeting will unfold according to the agenda.
• Let's wait and see how things unfold before making a decision.
• I have a feeling this party is going to unfold into something epic.
• As time passes, the true meaning of his words will slowly unfold.

adjective describing two or more things as not being identical or the same

• The twins were unidentical in appearance, making it difficult for people to tell them apart.
• Those two cars are unidentical - one is a sedan and the other is a SUV.
• I can't believe they're siblings, they look totally unidentical.
• The two political parties had unidentical views on the issue, causing a divide among the voters.

adjective relating to or characterized by unity

• The country has a unitary system of government where all power is centralized in the national government.
• In a unitary system, the central government has all the power.
• Unitary governments are like the boss of all bosses.
• The CEO is like a unitary leader, making all the decisions for the company.

adjective Describing something that has not been measured or quantified

• The impact of climate change on biodiversity is still largely unmeasured.
• Her talent is unmeasured, she's truly one of a kind.
• His level of coolness is unmeasured, he's just too chill.
• The depth of her love for him is unmeasured, it knows no bounds.

verb to separate or disentangle something that is twisted or knotted

• It took hours to untangle the complex legal documents.
• Can you help me untangle these wires?
• I need to untangle this mess before my boss finds out.
• She needed time to untangle her thoughts before making a decision.

adjective describes something that does not change or vary

• The scientist observed the unvarying pattern in the data collected over several months.
• The weather in this city is unvarying, it's always sunny and warm.
• Her taste in music is unvarying, she only listens to one genre.
• His unvarying dedication to his work earned him a promotion.

verb present participle form of the verb 'vanish', meaning to disappear suddenly or completely

adjective describing a process or event that disappears or fades away quickly

• The vanishing of certain species is a concerning issue in the field of conservation biology.
• Have you noticed the vanishing of old buildings in our neighborhood?
• I can't believe how fast the snacks are vanishing at this party!
• Her smile was like a vanishing dream, fleeting yet unforgettable.

noun a word that modifies a verb, an adjective, or another adverb

adverb in a way that is subject to change or variation

• The results of the experiment were variably distributed across the different groups.
• Her mood can be variably influenced by the weather.
• The prices at that store are variably high, depending on the day of the week.
• His opinions on the matter are variably colored by his personal experiences.

verb to change or differ in some way

adjective varied; diverse

adverb variously; in various ways

• The results of the experiment may vary depending on the conditions.
• The prices of these items can vary a lot from store to store.
• Her mood can vary from one minute to the next, you never know what you're gonna get.
• The opinions on this matter vary like the colors of a rainbow, everyone sees it differently.

verb to change or differ in some way

adjective showing diversity or differences

• The experiment yielded results with varying levels of accuracy.
• The colors of the flowers are all different shades, varying from light to dark.
• The party had a mix of music genres, varying from hip hop to electronic.
• Her mood was like a pendulum, constantly varying between highs and lows.

noun a point where two or more lines meet; the highest point; the top or apex

• In geometry, a vertex is a point where two or more lines, edges, or rays meet.
• The vertex of the triangle is at the top.
• Let's meet at the vertex of the park later.
• The decision to invest in new technology was the vertex of their success.

adverb used to indicate that the reverse of what is stated is true

preposition used to indicate that the positions of two elements are reversed

conjunction used to indicate that the order of two elements has been reversed

• In a scientific experiment, increasing the temperature led to an increase in pressure, and vice versa.
• I always check the weather forecast before making plans, and vice versa.
• I told her I like her, and vice versa, so we're going on a date next week.
• When it comes to relationships, communication is key - if one person is not willing to listen, then vice versa, the relationship will suffer.

adjective clearly and precisely described or outlined

• The mathematical theorem has a well-defined proof that has been verified by multiple experts.
• The instructions for assembling the furniture are well-defined, so it should be easy to put together.
• His goals for the project are well-defined, so he knows exactly what he needs to do.
• In her well-defined argument, she clearly outlined all the reasons why the policy should be changed.

adjective describing something that is firmly or securely placed or positioned

• The well-set foundation of the building ensured its stability during the earthquake.
• The well-set table looked beautiful with all the fancy dishes and cutlery.
• His muscles were so well-set, he could easily lift heavy weights.
• The well-set plan for the project ensured its success from the beginning.

noun a period of time

conjunction used to introduce a contrast or a change of direction in a sentence

• While I appreciate your effort, the results are not satisfactory.
• I'll be at the park while you finish up your homework.
• I was chilling at the beach while you were stressing about work.
• While she may seem tough on the outside, she is actually very kind-hearted.

noun a word used to identify any of a class of people, places, or things

verb a word used to describe an action, state, or occurrence

adjective a word that describes or modifies a noun or pronoun

adverb a word that modifies or qualifies an adjective, verb, or other adverb

pronoun a word that can function by itself as a noun phrase and that refers either to the participants in the discourse or to someone or something mentioned elsewhere in the discourse

preposition a word governing, and usually preceding, a noun or pronoun and expressing a relation to another word or element in the clause

conjunction a word used to connect clauses or sentences or to coordinate words in the same clause

interjection a word or phrase that expresses a strong emotion

• X marks the spot where the treasure is buried.
• Hey, can you show me where X is on the map?
• I heard there's some good stuff hidden at X.
• In this equation, X represents the unknown variable.

noun a German word meaning 'approach' or 'starting point', commonly used in mathematics and physics to describe a method or technique for solving a problem

• The physicist proposed a new ansatz for solving the complex equations.
• The scientist came up with a new ansatz to tackle the problem.
• I'm gonna try a different ansatz and see if it works.
• She approached the situation with a fresh ansatz, thinking outside the box.

noun a branch of mathematics that deals with the rates at which quantities change

• Differential calculus is a branch of mathematics that deals with the study of rates at which quantities change.
• I struggled with differential calculus because it involved a lot of complicated equations.
• Differential calculus is like trying to figure out how fast things are changing in math.
• Mastering differential calculus is like unlocking the secrets of how things evolve and transform in the world of mathematics.

noun a mathematical concept used in calculus to find the antiderivative of a function

adjective describing the type of integral that does not have specified limits of integration

• The process of finding the indefinite integral of a function involves finding the antiderivative of that function.
• When you're looking for the indefinite integral of a function, you're basically trying to find the original function that it came from.
• Dude, I spent hours trying to crack that indefinite integral problem.
• Finding the indefinite integral is like unraveling a mystery to reveal the hidden function within.

noun a cardinal number represented in the U.S. by 1 followed by 30 zeros, and in Great Britain by 1 followed by 54 zeros.

• The estimated number of stars in the universe is around one nonillion.
• I can't even imagine a nonillion of anything, it's just too big!
• That party was packed, there must have been a nonillion people there!
• Winning the lottery felt like I had a nonillion dollars in my bank account.

noun a cardinal number represented in the U.S. by 1 followed by 27 zeros, and in Great Britain by 1 followed by 48 zeros

• The estimated number of stars in the universe is around one octillion.
• I heard that Jeff Bezos has like an octillion dollars or something.
• I bet there are like octillion bugs in that old barn.
• Her patience seemed to be at an octillion when dealing with difficult customers.

noun a cardinal number represented in the U.S. by 1 followed by 21 zeros, and in Great Britain by 1 followed by 36 zeros.

• The estimated number of stars in the universe is in the order of a sextillion.
• I heard that Jeff Bezos is worth like a sextillion dollars or something crazy like that.
• I bet a sextillion bucks that he won't show up to the party.
• Her love for him was like a sextillion times stronger than anything she had ever felt before.

adjective describing something that goes in all directions or angles

adverb in a manner that goes in all directions or angles

• The scientist explained the quaquaversal movement of pollen grains in plants during his lecture.
• I watched a cool video of a quaquaversal waterfall on social media.
• The skateboarder attempted a quaquaversal trick at the skate park.
• Her thoughts were all over the place, moving quaquaversal in her mind.

adverb in a manner that is disappearing or becoming imperceptible

• The probability of this event occurring is vanishingly small.
• There's a vanishingly slim chance that he'll show up on time.
• I'm vanishingly broke after splurging on concert tickets.
• Her hopes of winning the competition were vanishingly faint.

adjective Relating to or involving pairs

adverb In a pairwise manner; considering each possible pair in a group

• The algorithm compares each data point pairwise to determine similarities.
• The app will show you pairwise comparisons of different products.
• Let's break it down into pairwise comparisons to make it easier to understand.
• The artist carefully arranged the colors in a pairwise fashion to create a harmonious composition.

noun A unit set refers to a collection of distinct objects, considered as a single entity or element.

• The unit set of all prime numbers is denoted by the symbol P.
• In math class, we learned about the unit set of prime numbers.
• I totally aced the quiz on the unit set of prime numbers.
• Each member of the team is like a unit set, working together towards a common goal.

noun a quintic equation or function

adjective referring to a mathematical expression or function of the fifth degree

• The mathematician presented a proof for the quintic equation during the conference.
• I struggled with understanding the quintic function in math class.
• That quintic problem on the test was a real doozy.
• Her emotions were like a quintic curve, constantly fluctuating and unpredictable.

noun a repeating pattern of shapes that fit perfectly together without any gaps or overlaps

• The artist created a beautiful tessellation pattern using geometric shapes.
• I love how the tiles in the bathroom tessellate perfectly.
• Check out the cool tessellation on that building's facade!
• The intricate tessellation of thoughts in her mind was both confusing and fascinating.

adjective not able to be solved or explained

• The mathematician claimed that the problem was unsolvable with current technology.
• I tried to solve that puzzle for hours, but it's just unsolvable.
• That math question is totally unsolvable, dude.
• The mystery of her disappearance seemed unsolvable to the detectives.

noun a mathematical method or process of finding the area of a figure by multiplying its dimensions

• The mathematician explained the concept of quadrature in great detail during the lecture.
• I still don't understand what quadrature means, can you explain it to me in simpler terms?
• Quadrature is like when you have to figure out the area of a weird shape in math class.
• The artist used quadrature to create a sense of depth and dimension in the painting.

preposition a word governing, and usually preceding, a noun or pronoun and expressing a relation to another word or element in the clause

• The success of a project relies on effective communication among team members.
• The taste of a homemade meal is always better than store-bought.
• The vibe of a party last night was lit!
• The weight of a secret can be burdensome.

noun A set of three positive integers a, b, and c, such that a^2 + b^2 = c^2, representing the sides of a right triangle

adjective Describing a set of three integers that satisfy the Pythagorean theorem

• A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2.
• Hey, did you know that 3, 4, 5 is a Pythagorean triple?
• Yo, check out this sick Pythagorean triple I just found: 5, 12, 13!
• In life, sometimes finding the right balance is like discovering a Pythagorean triple - everything just fits together perfectly.

noun A word that represents a person, place, thing, or idea. In this case, 'number' is a noun referring to a mathematical quantity.

adjective A word that describes or modifies a noun. In this case, 'deficient' is an adjective describing the type of number.

• A deficient number is a number that is greater than the sum of its proper divisors.
• If a number is bigger than the sum of its factors, it's called a deficient number.
• A deficient number is like when you have less money than you owe - not enough to cover it all.
• In life, feeling like a deficient number can be discouraging, but it's important to remember our worth is not defined by external measures.

adjective relating to or characterized by injection, especially denoting a function in which each element of the domain is mapped to a distinct element in the codomain

• The function is injective if each element in the domain maps to a unique element in the codomain.
• An injective function means that each input has its own distinct output.
• If the function is injective, it means each number gets its own special spot.
• Being injective is like having a one-to-one correspondence between two sets.

noun a group of one thousand things, especially years

• A chiliad is a term used to describe a group of one thousand things.
• I've been collecting stamps for a chiliad now.
• Let's grab a chiliad of snacks for the road trip.
• The chiliad of stars in the night sky was a breathtaking sight.

noun a number that is equal to the sum of its proper divisors, excluding itself

adjective describing the quality of being exact or without fault

• A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding itself.
• A perfect number is a cool math thing where the number equals the sum of its divisors.
• Dude, did you know about perfect numbers? They're like, totally awesome!
• In a world of imperfect numbers, a perfect number shines like a rare gem.

noun a point on a curve at which the curve changes from increasing to decreasing, or vice versa

• The company reached an inflection point where they needed to reevaluate their business strategy.
• Once we hit that inflection point, things really started to change around here.
• Dude, that was the inflection point of the whole situation.
• The argument reached an inflection point when both parties refused to compromise.

noun the quality of being separate or distinct

• The concept of discreteness is crucial in the field of mathematics.
• We need to maintain discreteness when handling sensitive information.
• Let's keep things on the down-low to ensure discreteness.
• The artist's use of discreteness in her brush strokes created a sense of mystery in the painting.

noun a mathematical concept used in the study of differential equations, named after the Russian mathematician Sergei Wronski

• The Wronskian is a mathematical concept used to determine linear independence of solutions to a differential equation.
• I had to calculate the Wronskian to check if the solutions were independent.
• The Wronskian is like a compatibility test for functions in differential equations.
• The Wronskian is like a detective that solves the mystery of linear independence in differential equations.

adjective describing a quality or attribute of a noun, in this case, 'multi-dimensional' describes something having multiple dimensions

• The research project aims to explore the multi-dimensional aspects of climate change.
• The new video game has a multi-dimensional storyline that keeps players engaged for hours.
• Her fashion sense is so multi-dimensional, she can pull off any look effortlessly.
• The artist's paintings are multi-dimensional, each stroke of the brush adding depth and meaning to the overall piece.

noun a word that represents a person, place, thing, or idea

verb a word that expresses an action, occurrence, or state of being

adjective a word that describes or modifies a noun or pronoun

preposition a word that shows the relationship between a noun (or pronoun) and other words in a sentence

• The artist's sculptures have form and structure that captivate viewers.
• I love how these cookies have form and hold their shape while baking.
• Dude, your dance moves totally have form, you should join a crew!
• Her arguments always have form and logic, making them very convincing.

noun abbreviation for Diabetes Insipidus Association

• Dia is a term used in Spanish to refer to 'day'.
• I'll see you dia after tomorrow.
• Let's hang out dia and chill.
• The new project deadline is looming like a dark cloud over our heads, ticking away like the passing of dia.

noun a subject of study that involves the use of numbers, quantities, and shapes to solve problems

• The study of math is essential for understanding complex scientific theories.
• I struggle with math homework because I find it challenging.
• I aced my math test, I'm a math genius!
• Life is like a math problem, you need to solve it step by step to reach the answer.

noun a unary operation or function

adjective relating to or consisting of a single element or component; monadic

• In mathematics, a unary operation is an operation with only one input.
• The unary function takes a single argument and returns a value.
• I only need to pass in one parameter for the unary method.
• His decision was a unary choice with no room for negotiation.

noun A quantity on which an operation is to be done in mathematics or logic

• In mathematics, an operand is a quantity on which an operation is performed.
• The operand in this equation is the number on the left side.
• Dude, just plug in the operand and you'll get the answer.
• The operand in this situation is the key factor that determines the outcome.

noun a threefold quantity or thing

verb to become three times as much or as numerous

• The company reported a tripling of profits compared to last year.
• I heard that sales are tripling since they launched the new product.
• That new restaurant is tripling in popularity among young people.
• Her confidence was tripling as she aced each exam.

noun a number that is equal to 10 raised to the power of a googol, or 10^(10^100)

• A googolplex is a very large number, specifically 10 to the power of a googol.
• Dude, have you ever heard of a googolplex? It's like, a crazy huge number.
• That party had a googolplex amount of people, it was insane!
• Her love for him was immeasurable, like a googolplex of affection.

adjective exaggerated or overstated

• The scientist used hyperbolic language to describe the potential impact of climate change.
• She always exaggerates with hyperbolic statements about her accomplishments.
• I can't stand when people use hyperbolic expressions to sound cool.
• The movie's hyperbolic special effects made it hard to believe in the storyline.

adverb in a parallel manner

• The two projects are running parallelly to ensure efficient completion.
• I'm working on two assignments parallelly to get them done faster.
• I'm juggling multiple tasks parallelly right now.
• Her thoughts were running parallelly, making it hard for her to focus on one thing at a time.

noun a structure or object that is ring-shaped

adjective relating to or shaped like a ring

• The annular eclipse was visible from certain parts of the world.
• Did you see the cool annular eclipse yesterday?
• That annular eclipse was lit!
• The annular design of the building symbolizes unity and continuity.

adjective relating to or involving exchange or substitution of two mathematical quantities so that the result is the same regardless of the order in which the quantities are taken

• In mathematics, addition is a commutative operation, meaning the order of the numbers does not affect the result.
• When adding numbers, it doesn't matter which one you start with because addition is commutative.
• Dude, you can switch the numbers around when adding them - it's commutative!
• Just like how rearranging the order of ingredients in a recipe doesn't change the final dish, addition is commutative in math.

noun BODMAS stands for Brackets, Orders (i.e. powers and square roots, etc.), Division and Multiplication, Addition and Subtraction. It is a rule used to decide the order of operations in mathematics.

• In mathematics, the order of operations is typically remembered using the acronym BODMAS.
• Remember to use BODMAS when solving math problems to get the correct answer.
• BODMAS is like the math ninja code that helps you solve equations like a boss.
• Just like following BODMAS in math, sometimes in life we need to prioritize tasks in a certain order to be successful.

noun LCM stands for Least Common Multiple, which is the smallest multiple that two or more numbers have in common.

• The least common multiple (LCM) of 12 and 18 is 36.
• To find the LCM of two numbers, just multiply them together.
• LCM is like finding the boss level of multiplication.
• In a group project, the LCM represents the common ground where everyone's ideas align.

noun a person or thing that is not in a straight line or course

adjective not consisting of or bounded by a straight line or lines

• The nonliner nature of the data made it difficult to analyze using traditional statistical methods.
• I can't make sense of this nonliner graph, it's so confusing.
• This nonliner stuff is way over my head, I don't get it at all.
• The nonliner plot of the movie kept me on the edge of my seat, never knowing what would happen next.

noun a term used in mathematics to refer to the x-coordinate of a point on a graph or coordinate plane

• The abscissa represents the horizontal position of a point on a graph.
• The abscissa is just the x-coordinate on the graph.
• Forget about the abscissa, just focus on where it is on the x-axis.
• In life, the abscissa can symbolize our starting point or origin.

noun the plural form of abscissa, which is a coordinate measured along the horizontal axis in a Cartesian coordinate system

• The abscissae on the graph represent the values of the independent variable.
• The points on the x-axis are called abscissae.
• Plot the data points on the horizontal line, those are the abscissae.
• In the journey of life, the abscissae mark the milestones we achieve.

noun the horizontal coordinate in a two-dimensional Cartesian coordinate system

• The abscissas represent the horizontal coordinates of points on a graph.
• You just need to plot the abscissas along the x-axis.
• Make sure you don't mix up the abscissas with the ordinates.
• The abscissas of success are hard work and determination.

noun The word 'abscissio infiniti' is a noun referring to a mathematical term used in calculus to describe an infinite division or subdivision of a line segment.

• The concept of abscissio infiniti is often used in advanced mathematics to describe infinite values on a coordinate plane.
• I heard that abscissio infiniti is some fancy math term for infinity on a graph.
• Ab-infiniti is like when the x-axis goes on forever, man.
• Her love for him seemed to stretch into abscissio infiniti, never-ending and boundless.

noun a layer of cells in a plant that is actively separating or being separated from the plant body

• The absciss layer of a plant is responsible for the shedding of leaves.
• The absciss layer is like the plant's way of saying goodbye to its leaves.
• When the absciss layer kicks in, it's time for the leaves to peace out.
• Just like how the absciss layer lets go of leaves, sometimes we need to let go of things in our lives too.

noun A noun is a word that represents a person, place, thing, or idea. In this case, 'absolute error' is a noun phrase that refers to the total amount of error without regard to its direction.

adjective An adjective is a word that describes or modifies a noun. In this case, 'absolute' is an adjective that emphasizes the error without considering its direction.

• The absolute error of the measurement was calculated to be 0.5 units.
• The absolute error in our estimate was only half a unit.
• We were off by like, just a smidge, the absolute error was barely noticeable.
• The absolute error in his judgment was glaringly obvious to everyone except himself.

noun a word that represents a person, place, thing, or idea

adjective a word that describes or modifies a noun or pronoun

• In order to ensure success, we must strive to work at the absolute minimum level of error.
• I always aim to do the absolute minimum required for my assignments.
• I'm just gonna do the bare minimum, no need to go above and beyond.
• He reached his absolute minimum in terms of motivation and productivity.

noun a word or phrase that refers to a person, place, thing, event, substance, or quality

adjective a word that describes or gives more information about a noun

• In mathematics, an absolute term is a constant term that is not dependent on any variables.
• An absolute term is just a number that doesn't change in the equation.
• Absolute term is like the boss of the equation, it stays the same no matter what.
• In life, happiness can be seen as an absolute term that remains constant despite external circumstances.

noun a mathematical concept that represents the magnitude of a real number without regard to its sign

adjective describing something that is complete and total

• In mathematics, the absolute value of a number is its magnitude without considering its sign.
• The absolute value of a number is just how far it is from zero, no negative nonsense.
• Forget about the negative stuff, the absolute value is all about the real deal.
• Sometimes we need to look at the absolute value of a situation to see the true impact it has on us.

noun a person, place, thing, or idea

adjective a word that describes or modifies a noun

• The absolute weight of the object is crucial in determining its stability.
• Dude, the absolute weight of that thing is insane!
• The absolute weight of the package is off the charts!
• The absolute weight of her decision was felt by everyone involved.

noun a branch of mathematics that deals with algebraic structures such as groups, rings, and fields

• The study of groups, rings, and fields falls under the branch of mathematics known as abstract algebra.
• Abstract algebra is all about studying structures like groups and rings.
• Abstract algebra may sound complicated, but it's really just a bunch of fancy math stuff.
• Understanding abstract algebra is like unlocking a secret code that reveals the hidden patterns in mathematics.

adverb in a way that is theoretical or not based on concrete reality

• The concept can be understood abstractly through mathematical equations.
• I can't grasp the idea of time travel when thinking about it abstractly.
• Dude, I can't even think about that abstractly, it's too much for my brain.
• She painted the scene abstractly, using bold colors and shapes to evoke emotion.

adjective relating to or characteristic of the Greek mathematician Diophantus of Alexandria, known for his work on algebraic equations

• The acleidian geometry is a branch of geometry that does not include the parallel postulate.
• I'm struggling to understand acleidian geometry in my math class.
• Acleidian stuff is so confusing, I can't wrap my head around it.
• Her mind works in an acleidian way, always finding unique solutions to problems.

noun a female given name of African origin

• Ada is a programming language that is widely used in the industry.
• I heard ada is a pretty cool language to learn.
• Have you checked out ada yet? It's pretty neat.
• In the world of coding, ada is like a hidden gem waiting to be discovered.

noun a rare or obsolete term for a state of being in a twisted or bent position

verb to twist or bend into a distorted position

• The chandelier was adangle, causing concern for its stability.
• The picture frame was adangle on the wall, so I straightened it out.
• The sign was adangle outside the store, making it look unprofessional.
• Her thoughts were adangle, unable to focus on one thing at a time.

noun a mathematical concept that refers to the number 0, which when added to any number, does not change the value of that number

• In mathematics, the additive identity is the number zero, denoted as 0.
• The additive identity is basically just the number zero.
• Zero is like the superhero of addition, it's the additive identity.
• Just like how zero is the starting point in math, the additive identity is the foundation of addition.

noun a mathematical term referring to the opposite of a given number when added to it results in a sum of zero

• In mathematics, the additive inverse of a number is the number that, when added to the original number, results in zero.
• If you add a number to its additive inverse, you will always get zero.
• The additive inverse of a number is like its 'opposite' in math.
• Finding the additive inverse is like finding the perfect balance point in a mathematical equation.

adverb describes how something is done in an additive manner

• The two chemicals react additively to produce a new compound.
• You can mix the ingredients additively to get the desired flavor.
• Just keep adding the toppings additively until it tastes right.
• His determination and hard work additively led to his success.

noun Adequation is a noun that refers to the act of making something adequate or suitable for a particular purpose.

• The adequation of the data to the research question was thoroughly examined.
• We need to make sure the data matches up with the research question.
• The data better be on point with the research question.
• The data and research question need to dance in perfect harmony.

noun abbreviation for adjective

• The architect designed a beautiful building with intricate adj detailing.
• I bought a cozy adj sweater for the winter.
• That new car is so adj, dude!
• Her words were sharp and adj, cutting through the tension in the room.

verb to adjudge or determine through a legal process

• The judge adjugates the case based on the evidence presented in court.
• The referee adjugates the game fairly.
• I can't believe how quickly she adjugates the situation.
• In a democratic society, the people adjugate the fate of their leaders through elections.

noun A mathematical term referring to the point that divides a line segment into two equal parts

adjective Describing something related to the midpoint or central point of a line segment

• The admedian of a triangle is a line segment that connects a vertex to the midpoint of the opposite side.
• I learned in math class that the admedian of a triangle is pretty important.
• Dude, the admedian thing in geometry is like mind-blowing!
• Just like the admedian balances out a triangle, finding balance in life is key.

verb to allow or make possible

preposition indicating that something is possible or capable of happening

• The scientific method is a systematic process admitting of no shortcuts.
• She has a strict rule admitting of no exceptions when it comes to punctuality.
• His style is very particular, admitting of no criticism from anyone.
• The painting was a masterpiece, admitting of no flaws in its composition.

preposition a word that shows the relationship between a noun or pronoun and other words in a sentence, in this case indicating direction to the right

• Tournez à droite au prochain carrefour pour rejoindre l'autoroute.
• Tu vas voir un grand arbre à droite, c'est là qu'il faut tourner.
• Y'a une soirée à droite ce soir, tu viens avec nous ?
• À droite, c'est là où se trouve la solution à ce problème complexe.

noun the act of changing or altering something

• Advolution is the process of moving something forward or progressing in a specific direction.
• I learned about advolution in my science class, it's like moving things forward.
• Advolution is all about pushing things ahead, you know?
• In life, we must embrace advolution to keep moving forward and growing.

noun Aeb is not recognized as a standard English word, so it does not have a specific definition as a noun.

• The company implemented an AEB system to enhance vehicle safety.
• I heard they installed a new AEB feature in the latest car model.
• Check out the AEB tech in this ride, it's lit!
• Having an AEB mindset can help you navigate through life's challenges more safely.

noun Aef is not a recognized English word, therefore it does not have a specific definition as a noun.

adjective Aef is not a recognized English word, therefore it does not have a specific definition as an adjective.

adverb Aef is not a recognized English word, therefore it does not have a specific definition as an adverb.

pronoun Aef is not a recognized English word, therefore it does not have a specific definition as a pronoun.

preposition Aef is not a recognized English word, therefore it does not have a specific definition as a preposition.

conjunction Aef is not a recognized English word, therefore it does not have a specific definition as a conjunction.

interjection Aef is not a recognized English word, therefore it does not have a specific definition as an interjection.

article Aef is not a recognized English word, therefore it does not have a specific definition as an article.

• The company implemented a new system called AEF to streamline their operations.
• I heard they're using some new software called AEF at work now.
• Have you tried out that AEF app yet? It's supposed to be really cool.
• Her words were like aef, cutting through the silence with precision.

noun an imaginary line around the Earth forming the great circle that is equidistant from the North and South Poles

• The equator, also known as the aequator, is an imaginary line that divides the Earth into the Northern Hemisphere and the Southern Hemisphere.
• I learned in geography class that the aequator is the line that goes around the middle of the Earth.
• Dude, did you know the aequator is like the ultimate halfway point on the planet?
• In life, finding balance is like standing on the aequator, navigating between extremes.

noun a word that represents a person, place, thing, or idea

preposition a word that shows the relationship between a noun or pronoun and other words in a sentence

• The efficiency of a machine is often considered a function of its design.
• Whether or not we go to the party is basically a function of who else is going.
• Your popularity is totally a function of how many likes you get on social media.
• Success can be seen as a function of hard work and determination.