| 11. | This is still infinity, but its not a countable infinity.
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| 12. | :A countable union of null sets is a null set.
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| 13. | Or maybe there is a reasonable classification for compact countable spaces?
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| 14. | Hence, they are discrete sets, so they are countable.
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| 15. | The operative word here is " countable ."
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| 16. | Since is countable, the Corollary implies that the union is countable.
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| 17. | Since is countable, the Corollary implies that the union is countable.
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| 18. | Every countable limit ordinal requires replacement for its construction analogously to ??.
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| 19. | It makes use of countable nonstandard models of Peano arithmetic.
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| 20. | \aleph _ 1 is the countable ( finite or denumerable ).
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