back to ideas for this text


Single Idea 18249

[from 'Thinking About Mathematics' by Stewart Shapiro, in 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy ]

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.