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Infinite No. Of Integers - Axiom Of Choice

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Posted by Herb S. on December 24, 2001 05:47:10 UTC

Proof that the number of integers is infinite.
1. Assume finite, then there must be a largest one.
2. Add 1 to the largest, you get a larger one, contradiction.
3. Original assumption is false, therefore number of integers is not finite (infinite).

The axiom of choice is as follows: Given an arbitrary collection of non-empty sets, there exists a set (the choice set), which has a non-empty intersection with every set in the original collection. If the collection is countable, it is a provable theorem. However, for non-countable collections, it cannot be proved or disproved.

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