a) If A and B are each countable sets, show that AUB is countable. (Hint: For each set, consider a sequence of all elements, and show how to splice the sequences together to make one sequence. Remember that the sets need not be disjoint.) b) Prove that the union of countably many finite sets is either countable or finite.
a) If A and B are each countable sets, show that AUB is countable. (Hint: For each set, consider a sequence of all elements, and show how to splice the sequences together to make one sequence. Remember that the sets need not be disjoint.) b) Prove that the union of countably many finite sets is either countable or finite.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CR: Chapter Review
Problem 2CC
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