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Full Idea
The claim that no number is greater than a million is confirmed by the first million test cases.
Gist of Idea
The first million numbers confirm that no number is greater than a million
Source
R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Intro')
Book Ref
Kaplan,R and Kaplan,E: 'The Art of the Infinite' [Penguin 2004], p.29
A Reaction
Extrapolate from this, and you can have as large a number of cases as you could possibly think of failing to do the inductive job. Love it! Induction isn't about accumulations of cases. It is about explanation, which is about essence. Yes!
| 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] |