| 41. | Above, " cardinality " was defined functionally.
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| 42. | ;Density : the minimal cardinality of a dense subset of a topological space.
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| 43. | This is a quite different statement, and is absurd for large finite cardinalities.
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| 44. | In particular, any finite Boolean ring has as cardinality a power of two.
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| 45. | This publication set out the modern cardinalities ).
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| 46. | Every aleph is the cardinality of some ordinal.
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| 47. | Since F is finite-dimensional, the basis X is of finite cardinality.
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| 48. | Then the cardinality of " B " is bounded below as follows:
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| 49. | Because Cantor implicitly assumed that cardinalities are linearly ordered, this case cannot occur.
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| 50. | :Note also that the rule above does not necessarily apply to infinite cardinalities.
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