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Axiom Of Choice

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Posted by Herb S. on April 27, 2001 04:04:06 UTC

Background - I am a retired mathematician.

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.

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.

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Here's the connection I see - paulm - April 27, 2001 - 17:52 UTC
- QM is one of example of discrete math. - alexander - April 27, 2001 - 21:33 UTC
  - I'm talking about finite; not discrete. (NT) - paulm - April 27, 2001 - 21:53 UTC
    - So, what is the diff: non-finite versus discrete? - alexander - April 27, 2001 - 22:13 UTC
      - Finite implies discrete; not the other way around. - paulm - April 28, 2001 - 00:42 UTC

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