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Full Idea
A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε.
Gist of Idea
Cauchy gave a formal definition of a converging sequence.
Source
Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4)
Book Ref
Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.181
A Reaction
The sequence is 'Cauchy' if N exists.
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] |