d 1 Let C = 10,1}. By definition C is the set of infinite sequences (a1,...
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d 1 Let C = 10,1}. By definition C is the set of infinite sequences (a1, a2, az,...) with an {0, 1} for all n. We verified in class that C is uncountable using Cantor's diagonal argument. Now consider the subset Co consisting of all sequences which eventually stabilizes to 0, i.e., Co= {(a1, a2, a3,): EN>0, an= 0 for all n > N} <C. Show that Co is countable. (Hint: use Problem 1 and rewrite Co = U-1 An as an infinite union of some subsets An such that each An is easily seen to be countable. For instance, take n=1 An= {(a1, a2, a3,..): am = 0 for all m n}.) d 1 Let C = 10,1}. By definition C is the set of infinite sequences (a1, a2, az,...) with an {0, 1} for all n. We verified in class that C is uncountable using Cantor's diagonal argument. Now consider the subset Co consisting of all sequences which eventually stabilizes to 0, i.e., Co= {(a1, a2, a3,): EN>0, an= 0 for all n > N} <C. Show that Co is countable. (Hint: use Problem 1 and rewrite Co = U-1 An as an infinite union of some subsets An such that each An is easily seen to be countable. For instance, take n=1 An= {(a1, a2, a3,..): am = 0 for all m n}.)
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Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
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