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Math Help - Proving finite sets

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    Proving finite sets

    Let f be a one-to-one function from A to B, with B being finite. Prove that A is finite.
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    Quote Originally Posted by Jdg6057 View Post
    Let f be a one-to-one function from A to B, with B being finite. Prove that A is finite.
    Suppose that f:A \mapsto B is injective.
    Note that means x \in A,\,y \in A\;\& \,x \ne y\, \Rightarrow \,f(x) \ne f(y)
    Using that property; \left( {\forall a \in A} \right)\left\{ {\{ f(a)\} } \right\} is collection of pair-wise disjoint subsets of B.
    If B is finite then what can you say about A?
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