===== Cauchy sequence =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $\langle X,d\rangle$ $\dots$ Metric space | 

| @#FFBB00: definiendum | @#FFBB00: $x\in \text{CauchySeq}(X) $ |

| @#55CCEE: context     | @#55CCEE: $x\in \text{InfSequence}(X) $ |

| @#DDDDDD: range       | @#DDDDDD: $\varepsilon\in \mathbb R,\ \varepsilon>0$ |
| @#DDDDDD: range       | @#DDDDDD: $n,m,N\in\mathbb N$ | 

| @#55EE55: postulate   | @#55EE55: $\forall\varepsilon.\ \exists N.\ \forall (n,m>N).\ d(x_n,x_m)<\varepsilon$ | 

==== Discussion ====
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Cauchy_sequence|Cauchy sequence]]
==== Parents ====
=== Context ===
[[Metric space]]
=== Requirements ===
[[Infinite sequence]]