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'fragments/reports', 'Begriffsschrift' and 'The Art of the Infinite'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
15712
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1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
15711
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The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
15714
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'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
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15715
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'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17855
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It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10607
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Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P]
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