Ideas from 'The Art of the Infinite' by R Kaplan / E Kaplan [2003], by Theme Structure
[found in 'The Art of the Infinite' by Kaplan,R and Kaplan,E [Penguin 2004,0-141-00886-5]].
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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Using Choice, you can cut up a small ball and make an enormous one from the pieces
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals
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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
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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
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'Distributive' laws say if you add then multiply, or multiply then add, you get the same result
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14. Science / C. Induction / 3. Limits of Induction
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The first million numbers confirm that no number is greater than a million
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