Combining Texts
Ideas for
'Intro to 'Philosophical Essays'', 'Philosophy of Mathematics' and 'Truth and Method'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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18100
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ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock]
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18101
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Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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18102
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A cardinal is the earliest ordinal that has that number of predecessors [Bostock]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
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18106
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Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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18095
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Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock]
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18099
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The number of reals is the number of subsets of the natural numbers [Bostock]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
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18093
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For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
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18110
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Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock]
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