Difference between revisions of "Cauchy criterion for convergence"
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Revision as of 07:24, 27 April 2015
If a sequence converges, it is the same as saying it matches the Cauchy criterion for convergence.
Cauchy Sequence
A sequence [math](a_n)^\infty_{n=1}[/math] is Cauchy if:
[math]\forall\epsilon>0\exists N\in\mathbb{N}:n> m> N\implies d(a_m,a_n)<\epsilon[/math]
Theorem
A sequence converges if and only if it is Cauchy
TODO: proof, easy stuff
