Cauchy sequence

Set

 context $\langle X,d\rangle$ $\dots$ Metric space
 definiendum $x\in \text{CauchySeq}(X)$
 context $x\in \text{InfSequence}(X)$
 range $\varepsilon\in \mathbb R,\ \varepsilon>0$ range $n,m,N\in\mathbb N$
 postulate $\forall\varepsilon.\ \exists N.\ \forall (n,m>N).\ d(x_n,x_m)<\varepsilon$

Discussion

Reference

Wikipedia: Cauchy sequence