Sentence examples for sequence whenever from inspiring English sources
A Banach space is said to have the Kadec-Klee property if for any sequence, whenever and, we have.
(ii) is a Cauchy sequence whenever for every with there is a natural number, such that for all.
It is denoted by or ; (ii) is a Cauchy sequence whenever for every with there is a natural number, such that for all ; (iii) is a complete cone normed space if every Cauchy sequence is convergent.
A real function f is continuous if and only if ( f ( x n ) ) is a convergent sequence whenever ( x n ) is. Regardless of limit, this is equivalent to the statement that ( f ( x n ) ) is Cauchy whenever ( x n ) is.
{ x n } is a Cauchy sequence whenever for each c ∈ A with 0 < c, there is a natural number N such that d ( x n, x m ) < c for all n, m ⩾ N. 3.
Definition 3.8 A sequence { s n } in an ordered metric space ( S, d X ) is called an order-Cauchy sequence, whenever there exists another sequence { x n } in ( X, ≽ X ) with x n ↓ 0 such that d X ( s m, s n ) ≼ X x n holds, for each n, and for every m ⩾ n. (3).
The first half-hour of the pilot is quite effective: the camera angles, spooky music and jumpy sequences (whenever a character appears, it is sudden and startling) are as frightening as those found in any horror movie, with an added twist of suspense.
Two -regular matrices and are said to be absolutely equivalent for a given class of sequences whenever (1.9).
We then prove an optimal sequence theorem that identifies a sequence that gives rise to an optimal processing time among all possible load distribution sequences, whenever such a sequence of load distribution exists.
Note that these definitions coincide with the notions of statistical convergence and of statistical Cauchy definitions for the real sequences whenever (mathbb{T}) is taken as the natural numbers.
A closer inspection of Fig. 1a suggests that the stripe patterns appeared upstream of a pure GA-sequence whenever its upstream end began with a certain stretch of poly(A) (i.e. with many black pixels).
