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.