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Prove that the collection of all intervals in R with endpoints in Qu{too) is countable. Recall that your goal is to show that the set of all intervals, not just the open ones, is countable. So you need to say that the set of all intervals can be written as the union of 5 subsets, namely the set of all (a,b) with a

Prove that the collection of all intervals in R with endpoints in Qu{too) is countable. Recall that your goal is to show that the set of all intervals, not just the open ones, is countable. So you need to say that the set of all intervals can be written as the union of 5 subsets, namely the set of all (a,b) with a

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...
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Prove that the collection of all intervals in R with endpoints in Qu{too) is countable.
Transcribed Image Text:Prove that the collection of all intervals in R with endpoints in Qu{too) is countable.
Recall that your goal is to show that the set of all intervals, not just the open ones, is countable. So you need to say that the set of all intervals can be written as the union of 5 subsets, namely the set of all (a,b) with a<b, the set of all (a,b] with a < b, the set of all [a,b) with a <b, the set of all [a,b] with a<=b, and the set consisting of just the emptyset, and then explain that each of the those is countable so their union is also countable.
Transcribed Image Text:Recall that your goal is to show that the set of all intervals, not just the open ones, is countable. So you need to say that the set of all intervals can be written as the union of 5 subsets, namely the set of all (a,b) with a<b, the set of all (a,b] with a < b, the set of all [a,b) with a <b, the set of all [a,b] with a<=b, and the set consisting of just the emptyset, and then explain that each of the those is countable so their union is also countable.
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