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]