Difference between revisions of "Cauchy criterion for convergence"

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 $$(a_n)^\infty_{n=1}$$ is Cauchy if:

$$\forall\epsilon>0\exists N\in\mathbb{N}:n> m> N\implies d(a_m,a_n)<\epsilon$$

Theorem

A sequence converges if and only if it is Cauchy

TODO: proof, easy stuff