10 ideas
15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |