more from Bertrand Russell

### Single Idea 14135

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers]

Full Idea

Real numbers are not really numbers at all, but something quite different; ...a real number, so I shall contend, is nothing but a certain class of rational numbers. ...A segment of rationals is a real number.

Gist of Idea

Real numbers are a class of rational numbers (and so not really numbers at all)

Source

Bertrand Russell (The Principles of Mathematics [1903], §258)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.270

Related Idea

Idea 18248
A real number is the class of rationals less than the number **[Russell/Whitehead, by Shapiro]**