Ideas from 'Continuity and Irrational Numbers' by Richard Dedekind [1872], by Theme Structure

[found in 'Essays on the Theory of Numbers' by Dedekind,Richard [Dover 1963,0-486-21010-3]].

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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

17611

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

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts

10572

A cut between rational numbers creates and defines an irrational number

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic

17612

Arithmetic is just the consequence of counting, which is the successor operation

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits

18087

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