Cauchy sequence englannista kaikille kielille

(mathematical analysis) Any sequence $x_{n}$ in a metric space with metric d such that for every $\epsilon >0$ there exists a natural number N such that for all $k,m\geq N$ , d(x_k, x_m) < ε .

\lim_{n,m→ ∞} \|x_n-x_m\|=0
In the case of the real line, every Cauchy sequence converges; that is, being a Cauchy sequence is sufficient to guarantee the existence of a limit. In the general case, however, this is not so. If a metric space does have the property that every Cauchy sequence converges, the space is called a complete metric space.

Monikko

Sanakirja.org