Single Idea 17611

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers]

Full Idea

It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity.

Gist of Idea

We want the essence of continuity, by showing its origin in arithmetic

Source

Richard Dedekind (Continuity and Irrational Numbers [1872], Intro)

Book Reference

Dedekind,Richard: 'Essays on the Theory of Numbers' [Dover 1963], p.2


A Reaction

[He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut'].