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# bijection

 Definition/Summary A function f: A $\rightarrow$ B is a bijection if for every b $\in$ B there is exactly one x $\in$ A such that f(x) = b. The inverse of a bijection f: A $\rightarrow$ B is the function g: B $\rightarrow$ A such that, for each b $\in$ B, g(b) is the unique element x $\in$ A such that f(x)= b. We write f$^{-1}$ for the function g. The inverse f$^{-1}$ of a bijection f is also a bijection, and its inverse is f. In other words: (f$^{-1}$)$^{-1}$ = f. A function is bijective if and only it is both an injection and a surjection.

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