In Real Numbers
A sequence
of real numbers is called Cauchy, if for every positive real number ε, there is a positive integer N such that for all natural numbers m, n > N
where the vertical bars denote the absolute value. In a similar way one can define Cauchy sequences of rational or complex numbers. Cauchy formulated such a condition by requiring to be infinitesimal for every pair of infinite m, n.
Read more about this topic: Cauchy Sequence
Famous quotes containing the words real and/or numbers:
“He that rebels against reason is a real rebel, but he that in defence of reason rebels against tyranny has a better title to “Defender of the Faith,” than George the Third.”
—Thomas Paine (1737–1809)
“The barriers of conventionality have been raised so high, and so strangely cemented by long existence, that the only hope of overthrowing them exists in the union of numbers linked together by common opinion and effort ... the united watchword of thousands would strike at the foundation of the false system and annihilate it.”
—Mme. Ellen Louise Demorest 1824–1898, U.S. women’s magazine editor and woman’s club movement pioneer. Demorest’s Illustrated Monthly and Mirror of Fashions, p. 203 (January 1870)