Re: what's wrong with this proof?
From: KRamsay (kramsay_at_aol.com)
Date: 11/20/04
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Date: 20 Nov 2004 22:47:27 GMT
In article <3128a7d.0411201126.4d8c085a@posting.google.com>, h56234@yahoo.com
(Matt H.) writes:
|Hausdorff's maximality theorem:
|Every nonempty partially ordered set P has a maximal linearly ordered
|subset.
|
|Proof:
|Let L be a linearly ordered subset of P. Let F be the collection of
|all linearly ordered subsets of P that are also supersets of L. Then
|the union of all the elements of F is a linearly ordered subset of P
|and is maximal.
The union is not always linearly ordered.
Keith Ramsay
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