Below, use a diagonal argument to show that the given set isuncountable.

The set I = {XER 0<x< 1}. Do this by using the one-to-one correspondence between elements of 1 and infinite decimal expansions 0.aa… that do not end with an infinite sequence of consecutive 9’s. Every element of I has exactly one such expansion, and every such expansion represents exactly one element of 1. For example, 0.5 could be written using the infinite decimal expansion 0.5000… or the expansion 0.49999…, but only the first is relevant in this problem, because the second ends with an infinite sequence of 9’s. In your proof, you just have to make sure that the decimal expansion you construct, in order to get a number not in the given list, doesn’t end with an infinite sequence of 9’s. Show transcribed image text The set I = {XER 0

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Answer to Below, use a diagonal argument to show that the given set is uncountable….