more from Richard Dedekind

Single Idea 18087

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits]

Full Idea

If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value.

Gist of Idea

If x changes by less and less, it must approach a limit


Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7

Book Reference

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.263

A Reaction

[Kitcher says he 'showed' this, rather than just stating it]