Equivalence Classes
x2X, prove existence and uniqueness of z2Zfor which (x;z) 2g fseparately. To prove uniqueness, suppose (x;z 1);(x;z 2) 2g f, and show that z 1 = z 2.) EQUIVALENCE RELATIONS AND WELL-DEFINEDNESS 5 We can translate the de nitions of injectivity and surjectivity in terms of the set f. De nition. Let f X Y be a function.
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