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]