21127 Study Guide - Quiz Guide: Surjective Function
16 Dec 2015
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Functions and their properties (1) let e be the set of even natural numbers. De ne d : n e {0} by d(n) = 2n 2. Let x, y n. suppose d(x) = d(y), so 2x 2 = 2y 2. Let z e {0} be given. Since z is even, we know k z. z = 2k. Since z 0, we can deduce k 0 (otherwise 2k = z < 0, a contradiction). Observe that a n since k n {0}, so a 1. Also, observe that d(a) = 2a 2 = 2(k + 1) 2 = 2k + 2 2 = 2k = z. Since d e {0} was arbitrary, this shows d is surjective. (2) find a function h : n p(n) that is injective. Then, prove that your function is not surjective. (notice that we"re telling you to do this, even though we don"t know what your function is going to be.
