Let A and B non-empty sets, A is infinite and B is countably infinite(∼N). Prove that if A is not countably infinite and B⊆A, then exists a bijection between A∖B and A.
I thought that i can use Schröder–Bernstein theorem, so i defined two injective function: id:A∖B→A and id:A→A∖B (id identity function) Is that conclude that there is a a bijection between A∖B and A? Thanks in advance.
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