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* A function f : X -> Y is bijective if and only if there exists a function g : Y -> X such that gof is the identity on X and fog is the identity on Y. In this case, g is uniquely determined by f and we call g the inverse function of f and write f -1 = g. * The bijective functions X -> X, together with functional composition, form a mathematical group, the symmetric group of X denoted by S(X). |
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