Difference between revisions of "Cauchy sequence/Short definition"
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Revision as of 13:54, 5 December 2015
Given a metric space [ilmath](X,d)[/ilmath] and a sequence [ilmath](x_n)_{n=1}^\infty\subseteq X[/ilmath] is said to be a Cauchy sequence[1][2] if:
- [ilmath]\forall\epsilon > 0\exists N\in\mathbb{N}\forall n,m\in\mathbb{N}[n\ge m> N\implies d(x_m,x_n)<\epsilon][/ilmath]
Notes
References
- ↑ Functional Analysis - George Bachman and Lawrence Narici
- ↑ Analysis - Part 1: Elements - Krzysztof Maurin
