Mathematical Analysis Terminology

noun a noun is a word that names a person, place, thing, or idea. In this case, 'convergence' is a noun as it refers to the act of converging or coming together.

adjective an adjective is a word that describes or modifies a noun. In this case, 'absolute' is an adjective that describes the type of convergence as being complete or total.

• The series exhibits absolute convergence, as the sum of the absolute values of the terms converges.
• The absolute convergence of the series means that the sum of the terms converges.
• When the series has absolute convergence, it means the terms add up nicely.
• The absolute convergence of the series is like having all the pieces of a puzzle fit perfectly together.

adjective Convergent is an adjective that describes something that comes together or meets at a point.

adverb Convergent can also be used as an adverb to describe the manner in which something is coming together.

• The series is absolutely convergent, meaning it converges regardless of the order of terms.
• The sum is absolutely convergent, so it doesn't matter how you add up the numbers.
• This sequence is totally convergent, no matter what.
• Her dedication to her work is like an absolutely convergent series, unwavering and constant.