**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 _{n} *X* from the standard set _{n} = {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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