Single Idea 14438

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

Full Idea

Every generalisation of number has presented itself as needed for some simple problem. Negative numbers are needed to make subtraction always possible; fractions to make division always possible; complex numbers to make solutions of equations possible.

Gist of Idea

New numbers solve problems: negatives for subtraction, fractions for division, complex for equations

Source

Bertrand Russell (Introduction to Mathematical Philosophy [1919], VII)

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.74


A Reaction

Doesn't this rather suggest that we made them up? If new problems turn up, we'll invent another lot. We already have added 'surreal' numbers.