Talk:Complete metric space/Definition: Difference between revisions
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imported>Paul Wormer (New page: I believe to have seen examples of sequences converging to an element outside the space, and I seem to remember that this gives a non-complete space. But I work from memory, I haven't ch...) |
imported>Richard Pinch m (Talk:Completeness (mathematics)/Definition moved to Talk:Complete metric space/Definition: Further disambiguate meaning within mathematics) |
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I believe to have seen examples of sequences converging to an element outside the space, and I seem to remember that this gives a non-complete space. But I work from memory, I haven't checked it.--[[User:Paul Wormer|Paul Wormer]] 08:55, 6 August 2008 (CDT) | I believe to have seen examples of sequences converging to an element outside the space, and I seem to remember that this gives a non-complete space. But I work from memory, I haven't checked it.--[[User:Paul Wormer|Paul Wormer]] 08:55, 6 August 2008 (CDT) | ||
:That's correct, the limit has to lie in the space itself, that's what I meant with "the sequence converges". You're right that it's better to make it explicit. -- [[User:Jitse Niesen|Jitse Niesen]] 10:17, 6 August 2008 (CDT) | |||
Latest revision as of 12:20, 4 January 2009
I believe to have seen examples of sequences converging to an element outside the space, and I seem to remember that this gives a non-complete space. But I work from memory, I haven't checked it.--Paul Wormer 08:55, 6 August 2008 (CDT)
- That's correct, the limit has to lie in the space itself, that's what I meant with "the sequence converges". You're right that it's better to make it explicit. -- Jitse Niesen 10:17, 6 August 2008 (CDT)