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

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