cauchy_sequence

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Cauchy sequence

Set

context

$\langle X,d\rangle$

$\dots$ Metric space

definiendum

$x\in \text{CauchySeq}(X)$

context

$x\in \text{InfSequence}(X)$

range	$\varepsilon\in \mathbb R,\ \varepsilon>0$
range	$n,m,N\in\mathbb N$

postulate

$\forall\varepsilon.\ \exists N.\ \forall (n,m>N).\ d(x_n,x_m)<\varepsilon$

Discussion

Reference

Wikipedia: Cauchy sequence

Parents

Context

Requirements

Infinite sequence