more from 'The Art of the Infinite' by R Kaplan / E Kaplan

Single Idea 15712

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number]

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 Reference

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.