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'fragments/reports', 'Infinity: Quest to Think the Unthinkable' and 'On the Introduction of Transfinite Numbers'
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14 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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10880
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Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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13489
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Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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12336
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A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
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10861
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Beyond infinity cardinals and ordinals can come apart [Clegg]
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10860
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An ordinal number is defined by the set that comes before it [Clegg]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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10854
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Transcendental numbers can't be fitted to finite equations [Clegg]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
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10858
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By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
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10853
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Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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10866
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Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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10869
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The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
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10862
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The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
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18179
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For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
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18180
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Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
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15925
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Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
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