Combining Texts

Ideas for 'works', 'Causal Powers' and 'Continuity and Irrational Numbers'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

15273

Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous' [Harré/Madden]

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]

15274

Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden]

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]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism

15211

There is not an exclusive dichotomy between the formal and the logical [Harré/Madden]