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Chapter 5: Bijections and Cardinality

Chapter 5: Bijections and Cardinality

pp. 128-163

Authors

, University of Toronto
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Summary

Given two infinite sets, is there a sensible way to decide which one is larger? For instance, if A is the set of even integers, and B is the interval [0, 1], is there a way to compare their sizes? In this section, we focus on such questions and introduce the notion of cardinality, which is used to describe “how many elements” a (potentially infinite) set has. This leads to some interesting and counterintuitive consequences. However, we must first prepare the ground by discussing injections, surjections, bijections, and related results.

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