Word Pronunciation & Dictionary

cauchy sequence

Word Rarity Very rare

Frequency: Zipf frequency 2.39 in modern English

Syllables: cauchy se-quence
IPA

35

Scrabble Score

14

Letters

2

Syllables

9

Unique Chars

Meaning

noun

Any sequence x_n in a metric space with metric d such that for every ϵ>0 there exists a natural number N such that for all k,m>N, d(x_k,x_m)<ϵ.

Example Sentences

"However, it is possible to derive topological results from statements about Cauchy sequences; for example, a subset A of the space of real numbers is closed if and only if each Cauchy sequence in A converges to some point of A."
"In the case of the real line, every Cauchy sequence converges; that is, being a Cauchy sequence is sufficient to guarantee the existence of a limit. In the general case, however, this is not so. If a metric space does have the property that every Cauchy sequence converges, the space is called a complete metric space."
"Cantor first redefined Cauchy sequences using rational numbers only.[…]Cantor's idea was to define the real number line as the collection of all (rational) Cauchy sequences."

Etymology

Named after French mathematician Augustin-Louis Cauchy (1789–1857), who made pioneering contributions to analysis.

Inflected Forms

Cauchy sequences (plural)

Derived Forms

Cauchy

Phrases

Cauchy convergence Cauchy filter Cauchy net Cauchy space

Frequently Paired Words

Cauchy convergence Cauchy filter Cauchy net Cauchy space

Questions

What does cauchy sequence mean?: Any sequence x_n in a metric space with metric d such that for every ϵ>0 there exists a natural number N such that for all k,m>N, d(x_k,x_m)<ϵ.
Where does cauchy sequence come from?: Named after French mathematician Augustin-Louis Cauchy (1789–1857), who made pioneering contributions to analysis.

How to pronounce cauchy sequence

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