Combining Texts

All the ideas for 'works (all lost)', 'The iterative conception of Set' and 'Continuity and Irrational Numbers'

expand these ideas     |    start again     |     specify just one area for these texts

---

5 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII

18192

Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy]

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 [Dedekind]

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 [Dedekind]

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

17612

Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]

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

18087

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