If we have two functions, $f:X\rightarrow X$ and $g:X\rightarrow X$ where $X$ is a finite set, why, if $g(f(x))=x$ for all $x\in X$, is it true that $f$ and $g$ are bijective?
Why do these functions have to be bijective?
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elementary-set-theory
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0This is closely related to your older question: http://math.stackexchange.com/questions/75880/if-g-circ-f-is-the-identity-function-then-which-of-f-and-g-is-onto-and-w/ – 2011-11-17