more on this theme | more from this thinker | more from this text
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 Ref
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]