more from B Russell/AN Whitehead

### Single Idea 18248

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts]

Full Idea

For Russell the real number 2 is the class of rationals less than 2 (i.e. 2/1). ...Notice that on this definition, real numbers are classes of rational numbers.

Gist of Idea

A real number is the class of rationals less than the number

Source

report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.122

Related Idea

Idea 14135
Real numbers are a class of rational numbers (and so not really numbers at all) **[Russell]**