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@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''"? [[User:Vijayaraghavan2k5|Vijay]] ([[User talk:Vijayaraghavan2k5|talk]]) 08:36, 11 January 2010 (UTC)
:Axel may not be watching anymore — he made that comment in 2006.
:Anyway, for ''A'' and ''B'' as defined, ''A'' doesn't ''have'' a largest element, and ''B'' doesn't have a smallest element. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 09:40, 11 January 2010 (UTC)
==Complete is the wrong word==
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