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Posted by Paul R. Martin on April 27, 2001 17:52:14 UTC

Hi Herb,

Thank you for your post. I hope you have the time to respond to this one so I can get straightened out.

>>>There is, and has been for almost a century, a school of thought in mathematics which tries to do without the axiom of choice.>Most mathematics can get along without it.>The axiom of choice is not really relevant to Cantor's ideas. You may have confused two results of Goedel. Specifically (1) the axiom of choice and (2) the continuum hypothesis (Cantor) are both independent of the axioms used to build up the natural number system. Moreover Goedel also showed them to be independent of each other.

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