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Full Idea
You have 1 and 0, something and nothing. Adding gives us the naturals. Subtracting brings the negatives into light; dividing, the rationals; only with a new operation, taking of roots, do the irrationals show themselves.
Gist of Idea
1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals
Source
R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Mind')
Book Ref
Kaplan,R and Kaplan,E: 'The Art of the Infinite' [Penguin 2004], p.25
A Reaction
The suggestion is constructivist, I suppose - that it is only operations that produce numbers. They go on to show that complex numbers don't quite fit the pattern.
| 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] |
| 15713 | The first million numbers confirm that no number is greater than a million [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] |
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |