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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 [Cantor ,by Lavine]
Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer ,by Korsgaard]
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]