Let S be a set. Suppose every function f: S → S also has an inverse function f−1. Prove or disprove that |S| must only be 0 or 1.
Let S be a set. Suppose every function f: S → S also has an inverse function f−1. Prove or disprove that |S| must only be 0 or 1.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 4E: 4. Let , where is nonempty. Prove that a has left inverse if and only if for every subset of .
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Let S be a set. Suppose every function f: S → S also has an inverse function f−1. Prove or disprove that |S| must only be 0 or 1.
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