(a) Prove that there exists a function f : Z → Z so that f is one-to-one but f is not onto. (b) Prove that there exists a function g : R → R so that g is onto but g is not one-to-one.
(a) Prove that there exists a function f : Z → Z so that f is one-to-one but f is not onto. (b) Prove that there exists a function g : R → R so that g is onto but g is not one-to-one.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 10E: 10. Let and be mappings from to. Prove that if is invertible, then is onto and is...
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