Single Idea 14431

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers]

Full Idea

Order must be defined by means of a transitive relation, since only such a relation is able to leap over an infinite number of intermediate terms. ...Without it we would not be able to define the order of magnitude among fractions.

Gist of Idea

The definition of order needs a transitive relation, to leap over infinite intermediate terms

Source

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

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.38