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I am trying to prove this (it looks true to me) :
Let $A,B $ be two sets. If there is a surjection $A\to B $ and a surjection $B\to A$ then $A $ and $B $ are in bijection.
I showed that is it equivalent to the following statement :
If there is an injection $A\to B $ and an injection $B\to A$ then $A $ and $B $ are in bijection.
But I am stuck, I don't see how to prove either.