I believe it is false, because an injective function never maps elements of the domain to the same element of its codomain, where as the surjective function can map an element of the codomain to any element in the domain.  I have some other explanations but they make little sense and are very messy, like this, can someone write a better explanation, or correct me entirely if I am wrong?
Is it true that for each set $M$ a given injective function $f: M \rightarrow M$ is surjective, too?  Can someone explain why it is true or not and give an example?
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