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

Revision as of 06:25, 26 March 2008

Revision as of 02:13, 15 April 2008

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Property 4 says that if you partition the set into two halves, then there must be a boundary point ''in the set''. This is not true for the rationals: take as ''A'' the set of all rationals smaller than √2 and as ''B'' the set of all rational above √2. Then all rationals are covered, since √2 is irrational, so this is a valid partition. There is no boundary point ''in the set of rational numbers'' that separates ''A'' from ''B'' however. [[User:AxelBoldt|AxelBoldt]] 02:09, 23 May 2006 (UTC)

* Ok, but could you clarify a little please... in as much as if you have your boundry, and A contains the elements less that that boundry, and B the elements greater than it, the the boundry is not in A or B. Probably missing something here, just can't see what.

**That isn't a partition. If c is in R, then for <nowiki>{A,B}</nowiki> to be a partition of R, c needs to be in A or in B. Eg, for property 4, c would have to be either the largest member of A or the smallest member B. [[User:Aij|Aij]] ([[User talk:Aij|talk]]) 02:13, 15 April 2008 (UTC)

==Complete is the wrong word==