Combining Texts
Ideas for
'fragments/reports', 'Introduction to Mathematical Logic' and 'Continuity and Irrational Numbers'
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9 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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17755
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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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17760
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Two infinite ordinals can represent a single infinite cardinal [Walicki]
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17757
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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 / 3. Nature of Numbers / g. Real numbers
17611
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We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
10572
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A cut between rational numbers creates and defines an irrational number [Dedekind]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
17612
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Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18087
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If x changes by less and less, it must approach a limit [Dedekind]
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