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'Defending the Axioms', 'Truth-makers' and 'The Art of the Infinite'
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5 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
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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
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'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
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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 / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
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