| 21. | Carl's Theorem states that the cardinality of the rational numbers.
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| 22. | Where A is some set with cardinality \ alpha.
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| 23. | Hence, the set has the same cardinality as.
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| 24. | There are two ways to define the " cardinality of a set ":
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| 25. | The 2nd element \ beth _ 1 is the cardinality of the continuum.
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| 26. | The set of computable numbers has the same cardinality as the natural numbers.
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| 27. | The cardinality of ? is denoted \ aleph _ 1 ( 23 problems.
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| 28. | Every set is of lower cardinality than the set of its subsets ".
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| 29. | In particular, every uncountable Polish space has the cardinality of the continuum.
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| 30. | This still leaves much ambiguity in the actual cardinality.
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