18 ideas
15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
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] |
17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |