Combining Texts

Ideas for 'Thinking About Mathematics', 'What is innate and why' and 'Continuity and Irrational Numbers'

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6 ideas

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

8763	The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]

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 / h. Reals from Cauchy

18249

Cauchy gave a formal definition of a converging sequence. [Shapiro]

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]