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# Cauchy sequence

## Definitions

### from Wiktionary, Creative Commons Attribution/Share-Alike License

• n. A sequence in a normed vector space such that the difference between any two entries can be made arbitrarily small by stipulating that the two entries be sufficiently far out in the sequence.
• n. A sequence in a metric space with metric d such that for every there exists a natural number N so that for every  : .

## Etymologies

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## Examples

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## Comments

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• A sequence x_n in a metric space with metric d such that for every \epsilon > 0 there exists a natural number N so that for every k, m \ge N : d(x_k, x_m) < \epsilon

March 21, 2011