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If A is a set, define the identity map on A by idд: A → A, id₁(a) = a. Then id is clearly a bijection. Lemma 1: Suppose
Posted: Mon Jul 11, 2022 12:50 pm
by answerhappygod
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If A is a set, define the identity map on A by idд: A → A, id₁(a) = a. Then id is clearly a bijection. Lemma 1: Suppose that f: A → B and g: B → A satisfy go f = idA, and fog=idg. Then f and g are bijections. Hint: By symmetry you can just prove that f is a bijection. Do this directly from the definitions (don't quote any other results).