Definition
We say that a sequence is Cauchy if , such that,
Proposition
A sequence is convergent if and only if it is a Cauchy sequence.
We say that a sequence (xn)n is Cauchy if ∀ε>0, ∃N>0 such that,
∣xn−xm∣<ε,∀n,m>N.A sequence (xn)n is convergent if and only if it is a Cauchy sequence.