Difference between revisions of "Complete (mathematics)"
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| − | In mathematics, a [[metric (mathematics)|metric space]] is said to be '''complete''' if all [[Cauchy sequences]] [[converge]]. Any compact (closed and bounded) metric space is complete. Other examples include the [[real numbers]] (with the Archimedean metric), the [[complex numbers]], and the [[p-adic numbers]]. | + | In [[mathematics]], a [[metric (mathematics)|metric space]] is said to be '''complete''' if all [[Cauchy sequences]] [[converge]]. Any compact (closed and bounded) metric space is complete. Other examples include the [[real numbers]] (with the Archimedean metric), the [[complex numbers]], and the [[p-adic numbers]]. |
[[Category:Topology]] | [[Category:Topology]] | ||
Revision as of 00:29, August 6, 2008
In mathematics, a metric space is said to be complete if all Cauchy sequences converge. Any compact (closed and bounded) metric space is complete. Other examples include the real numbers (with the Archimedean metric), the complex numbers, and the p-adic numbers.