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## Main Question or Discussion Point

in some books when we have a function f : A → B , and g : C → D , to prove that they are equal it proves that the domains are equal and the codomans are equal , in other words A=C and B=D , and that f(a) = g(a) , for all a element of A , I see that proving that codomains are equal is not necessarily important that is because f and g are sets of ordered pairs , that are subsets of A x B and C x D respectively , and I proved that they are equal if and only if A = C , and f(A) = f(C) , in other words A = C and f(a) = g(a) for all a element of A , is that right ???

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