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# Cardinality 2

Regarding the "Cardinality 2" definition:

You have written A >= B and B >= A, where you meant |A| >= |B| and |B| >= |A|.

Also, the fact that |A| >= |B| and |B| >= |A| together imply that there is a bijection between A and B is by no means obvious. I think you should mention that this is the Schroeder-Bernstein Theorem: http://planetmath.org/encyclopedia/SchroederBernsteinTheorem.html

Also, I think your definition is back-to-front: you should define two sets to have the same cardinality if there is a bijection between them, and then say that this is equivalent to |A| >= |B| and |B| >= |A| (by Schroeder-Bernstein), rather than the other way around.

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