Single Idea 14436

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

Full Idea

There is no maximum to the ratios whose square is less than 2, and no minimum to those whose square is greater than 2. This division of a series into two classes is called a 'Dedekind Cut'.

Gist of Idea

A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum

Source

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

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.69


Related Idea

Idea 14437 Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell]