MAT102H5 Study Guide - Quiz Guide: Empty Set, Bijection, Surjective Function
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MAT102H5 Full Course Notes
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Mat102f - intro. to mathematical proofs - fall 2018 - utm. Quiz 4 (version a) - november 29, 2018. Instructions: please have your student card ready for inspection, turn o all cellular phones, and read all the instructions carefully, do not start the quiz until instructed to do so. 1: prove that the following pairs of sets have the same cardinality. Theorem. (2 marks each) (a) the set n and s = {x r| x2 n}. To show that s and n have the same cardinality, we construct the following bijection from n onto s: Alternatively, we can explicitly de ne a bijection f that sends odd numbers n to the negative number q n+1. 2 , and even numbers n to the positive number p n. 2 . (b) the interval (0, 1) and the interval (0, ). These two sets have the same cardinality since there is a bijection f : (0, ) (0, 1).
