Combining Texts
Ideas for
'Unconscious Cerebral Initiative', 'Introduction to Mathematical Logic' and 'Knowledge and the Philosophy of Number'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17758
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Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
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Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
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17756
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The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
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Two infinite ordinals can represent a single infinite cardinal [Walicki]
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Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
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Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
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