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Aug 22, 2024 at 2:45 comment added Lucenaposition $\aleph_0\times\aleph_0$ and $\aleph_0$ have the same cardinality (this is provable in ZF). The statement "For all infinite sets $A$, there is a bijection between $A$ and $A\times A$" is equivalent to the axiom of choice.
Aug 22, 2024 at 2:43 comment added David K @Lucenaposition Is that true if $A$ is countable?
Aug 22, 2024 at 2:10 comment added Lucenaposition It is equivalent to the axiom of choice.
May 8, 2012 at 4:07 history made wiki Post Made Community Wiki by J. M. ain't a mathematician
May 2, 2012 at 17:22 history answered N. S. CC BY-SA 3.0