Talk:Cantor's first set theory article/Archive 1: Difference between revisions

Revision as of 16:34, 20 October 2014

Revision as of 02:00, 26 October 2014

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{{GA nominee|16:34, 20 October 2014 (UTC)|nominator=[[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]])|page=1|subtopic=Mathematics and mathematicians|status=onreview|note=}}

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Cantor's 2nd theorem seems obvious at first glance to many people, as we usually are unable to imagine a sequence that could completely fill a whole interval. However, there are sequences (like that of all positive rational numbers) whose set of [[accumulation point]]s equals a whole interval (or even whole ℝ₊; cf. the picture [[accumulation point|there]]). Mentioning this in the article might prevent novice readers from thinking "''Mathematicians make a big fuzz proving things that are obvious, anyway''", and might generally help to sharpen one's intuition about what a sequence ''can'' do in relation to an interval and what it ''cannot''. It would require, however, to explain the notion of an ''accumulation point'' (which is poorly represented in English Wikipedia in general). - [[User:Jochen Burghardt|Jochen Burghardt]] ([[User talk:Jochen Burghardt|talk]]) 11:52, 17 December 2013 (UTC)

{{Talk:Cantor's first uncountability proof/GA1}}