Wednesday, 16 March 2016

elementary set theory - Does there exist a bijection between sets AsetminusB and A?

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 BA, then exists a bijection between AB and A.



I thought that i can use Schröder–Bernstein theorem, so i defined two injective function: id:ABA and id:AAB (id identity function) Is that conclude that there is a a bijection between AB and A? Thanks in advance.

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