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An Introduction to Mathematical Reasoning by Peter J. Eccles

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14

Counting infinite sets

In Chapter 10 a non-empty set X was defined to have cardinality n, where n is a positive integer, when there is a bijection imagesn images X from the standard set imagesn = {1,2,…, n}. Such sets, together with the empty set, were defined as finite and all others as infinite.

We saw (Exercise 10.1) that, given a finite set X, another set Y is also finite of the same cardinality if and only if there is a bijection X Y. In this case we say ...

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