# Is the number of infinite subsets of Z equal to the size of R? [closed]

From Cantor we know that |R| = 2^|Z|. That is, |R| is equal to the number of subsets of Z. Is it also true that |R| is equal to the number of infinite subsets of Z?

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## closed as too localized by Todd Trimble♦, Peter Shor, J.C. Ottem, Joel David Hamkins, coudyMar 5 '11 at 20:22

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This question should be closed; it is more appropriate for math stack exchange. –  Todd Trimble Mar 5 '11 at 20:04

The set of subsets of $\mathbb{Z}$ can be seen as the set of all functions $f:\mathbb{Z}\to\{0,1\}$. And this last set can be seen as the set of all sequences of 0 and 1. With this last point of view, it is easy to see that there exists a bijection between this set and, for instance, the interval $[0,1]$.