structure for 'Mathematics'    |     alphabetical list of themes    |     expand these ideas

6. Mathematics / A. Nature of Mathematics / 3. Numbers / h. Reals from Cauchy

[defining real numbers using Cauchy sequences]

5 ideas
A real is associated with an infinite set of infinite Cauchy sequences of rationals [Lavine on Cantor]
Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Korsgaard on Brouwer]
Cauchy gave a formal definition of a converging sequence. [Shapiro]
Cauchy gave a necessary condition for the convergence of a sequence [Lavine]
Irrational numbers are the limits of Cauchy sequences of rational numbers [Lavine]