Single Idea 18250

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy]

Full Idea

The Cauchy convergence criterion for a sequence: the sequence S0,S1,... has a limit if |S(n+r) - S(n)| is less than any given quantity for every value of r and sufficiently large values of n. He proved this necessary, but not sufficient.

Gist of Idea

Cauchy gave a necessary condition for the convergence of a sequence

Source

Shaughan Lavine (Understanding the Infinite [1994], 2.5)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.33