Absolute Convergence

Pronunciation: /ˈæbsəˌlut kənˈvɜrʤəns/

Definitions of absolute convergence

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.

Example Sentences

A1 Absolute convergence means that a series of numbers always converges to the same value.

A2 In mathematics, absolute convergence refers to a series whose rearrangements always converge to the same sum.

B1 Understanding the concept of absolute convergence is essential in advanced calculus courses.

B2 The theorem states that if a series satisfies the condition of absolute convergence, then it converges.

C1 Mathematicians use absolute convergence to study the convergence properties of infinite series in great detail.

C2 The concept of absolute convergence plays a crucial role in the analysis of complex mathematical functions.

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.

Example Sentences

A1 Absolute convergence means that a series converges regardless of the order of its terms.

A2 In mathematics, absolute convergence refers to a series whose rearrangement does not affect its convergence.

B1 Understanding the concept of absolute convergence is essential in advanced calculus courses.

B2 The theorem on absolute convergence allows us to manipulate series with confidence.

C1 The proof of absolute convergence involves intricate mathematical reasoning.

C2 Only a mathematician with a deep understanding of analysis can appreciate the beauty of absolute convergence.

Examples of absolute convergence in a Sentence

formal The series exhibits absolute convergence, as the sum of the absolute values of the terms converges.

informal The absolute convergence of the series means that the sum of the terms converges.

slang When the series has absolute convergence, it means the terms add up nicely.

figurative The absolute convergence of the series is like having all the pieces of a puzzle fit perfectly together.

Grammatical Forms of absolute convergence

• past tense: absolutely converged
• plural: absolute convergences
• comparative: more absolutely convergent
• superlative: most absolutely convergent
• present tense: absolutely converges
• future tense: will absolutely converge
• perfect tense: has absolutely converged
• continuous tense: is absolutely converging
• singular: absolute convergence
• positive degree: absolutely convergent
• infinitive: to absolutely converge
• gerund: absolutely converging
• participle: absolutely converged

Origin and Evolution of absolute convergence

First Known Use: 1824 year

Language of Origin: Latin

Story behind the word: The term 'absolute convergence' originated in mathematics to describe a series that converges regardless of the order in which its terms are summed.

Evolution of the word: Originally used in the context of mathematical analysis, the term 'absolute convergence' has since been adopted in various fields such as economics and physics to denote a state of convergence that is independent of any rearrangement of terms.