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 Reference
Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.181
A Reaction
The sequence is 'Cauchy' if N exists.