Talk:Partially ordered set: Difference between revisions

Revision as of 01:21, 9 January 2005

Revision as of 02:47, 9 January 2005

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Well, I might be wrong ;-) but I assumed that the first poster's proof was essentially the following: Suppose ''a'' < ''b''. We want to show that it is not the case that ''b'' < ''a''. Now assume that ''b'' < ''a'', then by transitivity, ''a'' < ''a'', but this is a contradiction by irreflexivity, therefore since assuming ''b'' < ''a'' leads to a contradiction, ''b'' < ''a'' must be false, QED. Is this not an example of "proof by contradiction? Don't the intuitionists reject this method of proof? [[User:Paul August|Paul August ]] [[User_talk:Paul August|&#9742;]] 01:09, Jan 9, 2005 (UTC)

'''Negated''' statements are "classical" (regular) so 'proofs by contradiction' are intuitionistically valid. [[User:DefLog|DefLog]] 02:47, 9 Jan 2005 (UTC)