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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 Ref
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'].
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |