Cauchy sequence

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Cauchy sequence

[kō·shē ′sē·kwəns]

(mathematics)

A sequence with the property that the difference between any two terms is arbitrarily small provided they are both sufficiently far out in the sequence; more precisely stated: a sequence {a_n } such that for every ε > 0 there is an integer N with the property that, if n and m are both greater than N, then | a_n-a_m | < ε.="" also="" known="" as="" fundamental="" sequence;="" regular="">

Cauchy sequence

(mathematics)

A sequence of elements from some vector space that converge and stay arbitrarily close to each other (using the norm definied for the space).

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In Section 2 we study some properties of f--statistical convergent and f--statistical Cauchy sequences, giving a characterization of Banach spaces in those terms.

2 On f--statistical convergence and f--statistical Cauchy sequences

In this section we try to make clear the role of Cauchy sequences in the setting of f--statistical convergence.

f-statistical convergence, completeness and f-cluster points

Also we find out the relation between [lambda]-statistical convergent and [lambda]-statistical Cauchy sequences in this spaces.

On generalized statistical convergence in random 2-normed spaces

122) that there exist Cauchy sequences which are not Mackey-Cauchy sequences.

Ford lemma for topological *-algebras/Fordi lemma topoloogiliste *-algebrate korral

m] are technically equivalence classes of Cauchy sequences of elements of [[?

Banach framed, decay in the context of localization

The constructivist takes real numbers as, say, Cauchy sequences of rationals (either equivalence classes thereof or certain canonical ones), but in the definition of 'Cauchy sequence', constructive quantifiers are to be understood.

One then speaks of 'constructive Cauchy sequences'; if Church's Thesis (CT) is accepted, these become identified with recursive Cauchy sequences, of which there are only countably many.

Given real numbers, x and y, generated by Cauchy sequences of rationals, <[x.

Mathematical constructivism in spacetime

1,l])(k, l [less than or equal to] u) are Cauchy sequences in (X, q).

On some I-convergent generalized difference lacunary double sequence spaces defined by orlicz functions/Espacos sequenciais duplos com diferenca lacunar generalizada I-convergentes definidos pela funcao de orlicz

1,l]) (k,l [less than or equal to] r) are Cauchy sequences in (X,q).

Some new generalized difference double sequence spaces via Orlicz functions

1,l])(k, l [less than or equal to] n) are Cauchy sequences in (X, q) Since (X, q) is complete, so there exists [x.

Some generalized Lacunary statistically difference double semi-normed sequence spaces defined by Orlicz function/Espacos sequenciais semi-normais duplos com diferenca estatistica lacunar generalizada definidos pela funcao de Orlicz