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* 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)
@AxelBoldt - In your example, why can't the boundary point be the largest rational in ''A'' or the smallest rational in ''B''? Then, all rationals less than the boundary will be in ''A'' and all rationals greater than the boundary will be in ''B''. Or am I misunderstanding the meaning of the word "every point" as "every point in ''R''"?
==Complete is the wrong word==
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