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Ideas for 'fragments/reports', 'Continuity and Irrational Numbers' and 'Philosophy of Arithmetic'

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7 ideas

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 / 3. Nature of Numbers / l. Zero

9837	0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units

9576	Multiplicity in general is just one and one and one, etc. [Husserl]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation

17444

Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]

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]