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I agree, it doesn't need to be in the first sentence, or even the first paragraph. But it should be documented nevertheless. [[User:AxelBoldt|AxelBoldt]] 14:42, 3 May 2006 (UTC)
==The rationals==
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:''(Could someone who understands explain why the set of rational numbers does not have property 4?)''
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)
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