Mathematical Proofs

adjective a word that describes or modifies a noun or pronoun, in this case, 'deductive' describes a type of reasoning that is based on logical conclusions

• The scientist used deductive reasoning to reach a logical conclusion based on the evidence.
• She's really good at figuring things out using deductive reasoning.
• Dude, I totally deduced that she was lying about her whereabouts.
• His deductive skills were like a well-oiled machine, always leading him to the right answer.

noun a logical fallacy in which the middle term in a syllogism is not distributed in either the major or minor premise

adjective describing the fallacy of undistributed middle

• The fallacy of undistributed middle occurs when the middle term in a syllogism is not distributed in either the major or minor premise.
• You can't just assume a connection between two things without properly distributing the middle term in your argument.
• Don't be fooled by that undistributed middle, it's just a sneaky way to make a false connection.
• Just like a bridge without supports, an argument with an undistributed middle will collapse under scrutiny.

noun a gesture or movement of the hand, especially one made to emphasize or express something

verb to make a gesture or movement with the hand, especially to emphasize or express something

• The scientist used a handwave to simplify the explanation for the general audience.
• She just handwaved the whole situation and didn't give us any details.
• He always handwaves his responsibilities and expects others to pick up the slack.
• The politician's promises were nothing but handwaves, with no real plans for implementation.

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

adjective A word that describes or modifies a noun

• A primitive Pythagorean triple is a set of three positive integers that satisfy the Pythagorean theorem and have no common divisor greater than 1.
• So basically, a primitive Pythagorean triple is just a set of three numbers that work in the Pythagorean theorem and don't share any big factors.
• Yo, check out this sick primitive Pythagorean triple I found - it's like the perfect combo of numbers for a right triangle.
• The relationship between the sides of a right triangle can be seen as a primitive Pythagorean triple, where each side plays a unique role in maintaining the triangle's balance.

adverb in a way that is contrary to reason or common sense

• The argument was refuted ab absurdo by pointing out the flaws in its logic.
• He tried to prove his point ab absurdo, but no one was convinced.
• She shut down his theory ab absurdo with a simple counterexample.
• The artist's painting challenged viewers to interpret it ab absurdo, leaving them puzzled and intrigued.

noun a contrary or opposing argument or viewpoint

• The judge ruled a contrario, stating that the evidence presented did not support the defendant's claim.
• She always argues a contrario, just to play devil's advocate.
• I see things a contrario, but that's just my opinion.
• Looking at the situation a contrario, it's clear that there are hidden motives at play.

noun a Latin phrase meaning 'to the point of absurdity', often used in logic and argumentation to demonstrate the absurdity of a certain claim or argument

• The philosopher argued his point ad absurdum, using logical reasoning to show the flaw in his opponent's argument.
• She took his joke ad absurdum, laughing until tears streamed down her face.
• The internet meme took the concept ad absurdum, turning a simple idea into a viral sensation.
• The artist pushed the boundaries of reality ad absurdum, creating a surreal masterpiece.

adverb used to express a conclusion for which there is stronger evidence than for a previously accepted one

• The evidence presented in the previous case is strong; a fortiori, it should be even more convincing in this instance.
• If she aced all her exams last semester, a fortiori she'll do even better this time around.
• If he can lift 200 pounds, a fortiori he can handle this small task.
• If she survived a difficult childhood, a fortiori she can overcome any obstacle in her path.