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Re: Inconsistency of the usual axioms of set theory
Posted:
Feb 24, 2009 4:03 PM
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On Feb 24, 12:26 am, omar.hosse...@gmail.com wrote:
> Consider ZF without the axiom of infinity, then you do can not assert
> the
> existence of an infinite set.
>
> Suppose X={x_0,x_1,x_2,...,x_n} be a set for which there exists a 1-1
> correspondence
> between X and some proper subset(s) of X, like y. This implies |y|=|X|
> =n+1
> (n is a natural number).
If X is finite, then there is no 1-1 correspondence between X and a
proper subset of X. That is proven, and famous in ordinary first-year
college mathematics as 'the pigeonhole principle'.
MoeBlee
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