Suppose that {An : n e N} is a family of sets (not necessarily pairwise disjoint) such that An is countable for every n. Prove that UnEN An is countable. (Hint: prove that there is a surjection f : N x N →Unen An and say why this is sufficient.)
Suppose that {An : n e N} is a family of sets (not necessarily pairwise disjoint) such that An is countable for every n. Prove that UnEN An is countable. (Hint: prove that there is a surjection f : N x N →Unen An and say why this is sufficient.)
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 15E: 15. Let be a binary operation on the non empty set . Prove that if contains an identity element...
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