Cauchy sequence/Short definition
From Maths
< Cauchy sequence
Revision as of 13:54, 5 December 2015 by Alec (Talk | contribs) (Created page with "Given a metric space {{M|(X,d)}} and a sequence {{M|1=(x_n)_{n=1}^\infty\subseteq X}} is said to be a ''Cauchy sequence''<ref name="FA">Functiona...")
Given a metric space (X,d) and a sequence (xn)∞n=1⊆X is said to be a Cauchy sequence[1][2] if:
- ∀ϵ>0∃N∈N∀n,m∈N[n≥m>N⟹d(xm,xn)<ϵ]
Notes
References
- Jump up ↑ Functional Analysis - George Bachman and Lawrence Narici
- Jump up ↑ Analysis - Part 1: Elements - Krzysztof Maurin
