Sentence examples for sequence tending to zero from inspiring English sources

Cauchy defined an infinitesimal in Cours d'Analyse (1827) in terms of a sequence tending to zero.

A sequence u tending to zero is called a rest bounded variation sequence (briefly (uin RBVS)), if it has the property sum_{m=k}^{infty}|Delta u_{m}|leq K u u_{k} for all natural numbers k (see [10]).

where is a sequence of positive numbers tending to zero.

where h n is a sequence of positive bandwidths tending to zero as n → ∞.

Define (K_{h}(x)=h^{-d}K(x/h)), where (h=h_{n}) is a sequence of positive bandwidths tending to zero as (nrightarrowinfty).

Thus { x n } is non-decreasing sequence tending to x and { y n } a non-increasing sequence tending to y.

which implies that is a non-decreasing sequence and does not tend to zero as.

Then there exist an integer (p inmathbb{N}^), a sequence ((varepsilon_{k}) >0), (varepsilon_{k}) tends to zero, and an extracted subsequence of (u_{k}) 's, again denoted ((u_{k})), such that (u_{k} in V p,varepsilon_{k})).

If N 0 < A, then the sequence N t monotonically tends to zero.

The main idea is to construct a sequence such that the sequence tends to 0 as.

Then there exist an integer p ∈ N ∗, a sequence ( ε K ) > 0, ε k tends to zero, and an extracted subsequence of u k 's, again denoted by ( u k ), such that u k ∈ V ( p, ε k, w ), where w is zero or a solution of (1.1).