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Let A be a finite set and let f be a surjection from A to itself....

Let A be a finite set and let f be a surjection from A to itself. Show that f is an injection.

Use Theorem 1, 2 and corollary 1.

Theorem 1 : Let B be a finite set and let f be a function on B. Then f has a right inverse. In other words, there is a function g: A->B, where A=f[B], such that for each x in A, we have f(g(x)) = x.

Theorem 2: A right inverse for a function is an injection

Corollary 1: An injection from a finite set to itself is a surjection

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