Abstract
We know quite a bit about cardinal numbers by now, but we still do not know what they are. Speaking vaguely, we may say that the cardinal number of a set is the property that the set has in common with all sets equivalent to it. We may try to make this precise by saying that the cardinal number of X is equal to the set of all sets equivalent to X, but the attempt will fail; there is no set as large as that. The next thing to try, suggested by analogy with our approach to the definition of natural numbers, is to define the cardinal number of a set X as some particular carefully selected set equivalent to X. This is what we proceed to do.
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© 1974 Springer Science+Business Media New York
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Halmos, P.R. (1974). Cardinal Numbers. In: Naive Set Theory. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1645-0_25
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DOI: https://doi.org/10.1007/978-1-4757-1645-0_25
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90104-6
Online ISBN: 978-1-4757-1645-0
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