Sunday, 12 July 2015

elementary set theory - Prove that if A is an infinite set then Atimes2 is equipotent to A

I want to prove that if A in an infinite set, then the cartesian product of A with 2 (the set whose only elements are 0 and 1) is equipotent to A.




I'm allowed to use Zorn's Lemma, but I can't use anything about cardinal numbers or cardinal arithmetic (since we haven't sotten to that topic in the course).



I read a proof of the fact that if a is an infinite cardinal number, then a+a=a, which is something similar to what I want to prove.



Any suggestions will be appreciated :)

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