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]].

Click on the Idea Number for the full details    |     back to texts     |     expand these ideas


6. Mathematics / A. Nature of Mathematics / 3. Numbers / g. Real numbers
We want the essence of continuity, by showing its origin in arithmetic
6. Mathematics / A. Nature of Mathematics / 3. Numbers / i. Reals from cuts
A cut between rational numbers creates and defines an irrational number
6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
Arithmetic is just the consequence of counting, which is the successor operation
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / m. Limits
If x changes by less and less, it must approach a limit