So if I have two sets A and B and if |A| = |B| and if function f is a function from A to B and is injective, how can I prove that it is also surjective?
Forgot to mention. A and B are finite sets.
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Think about the map $f:\mathbb N\to\mathbb N$ where $$f(x)=x+1$$It's injective but not surjective. The claim is only true if $|A|<\infty$. – Rushabh Mehta Nov 06 '19 at 05:58
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See this or this. – Rushabh Mehta Nov 06 '19 at 06:00