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]