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Full Idea
Cantor's theory of Cauchy sequences defines a real number to be associated with an infinite set of infinite sequences of rational numbers.
Gist of Idea
A real is associated with an infinite set of infinite Cauchy sequences of rationals
Source
report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite II.6
Book Ref
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.38
A Reaction
This sounds remarkably like the endless decimals we use when we try to write down an actual real number.
15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |