12 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] |
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| 5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| 6012 | We must choose in which of the virtues we wish to excel [Panaetius] |
| 6013 | Panaetius said we should live according to our natural starting-points [Panaetius, by Asmis] |
| 6014 | Panaetius identified courage with great-mindedness, preferring civic courage to military [Panaetius, by Asmis] |
| 5888 | Souls are born, since they are sensitive and inherited, so they must perish [Panaetius, by Cicero] |