Cauchy sequence
A sequence in a metric space is a Cauchy sequence if, for every real number , there exists a natural number such that whenever .
Likewise, a sequence in a topological vector space is a Cauchy sequence if and only if for every neighborhood of , there exists a natural number such that for all . These two definitions are equivalent when the topology of is induced by a metric.
Title | Cauchy sequence |
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Canonical name | CauchySequence |
Date of creation | 2013-03-22 11:55:04 |
Last modified on | 2013-03-22 11:55:04 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 10 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 54E35 |
Classification | msc 26A03 |
Synonym | fundamental sequence |
Related topic | MetricSpace |