Combining Texts

All the ideas for '11: Book of Kings 1', 'The Art of the Infinite' and 'fragments/reports'

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8 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

15717

Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

15712

1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

15711

The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / n. Pi

17914

He made a molten sea, which was ten cubits across, and thirty cubits round the edge [Anon (Kings)]

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]

13. Knowledge Criteria / D. Scepticism / 1. Scepticism

3061	Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]

14. Science / C. Induction / 3. Limits of Induction

15713

The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]