Sentence examples for a increasing sequence from inspiring English sources

For let be a increasing sequence and be a decreasing sequence.

where If is a increasing sequence and is a decreasing sequence, the above inequality is also valid.

if ({x_{n}}) is a increasing sequence in A with (x_{n}to xin A) as (ntoinfty), then (x_{n}preceq x) for all (ninmathbb{N}).

Since ({a_{n}}) is an increasing sequence in A and (a_{n}to a), by hypothesis (iv), (a_{n}preceq a), ∀n.

Thus, ({f^{n}(a):ninBbb{N}cup{0}}) is an increasing sequence of iterates which is bounded, and so the least upper bound of ({f^{n}(a):ninBbb{N}cup{0}}) exists.

Because the optimal total transmission power is a constant or an increasing sequence, Po 3 changes simultaneously with P1, P2, and P3.

Assume that either f is continuous or that A ¯ 0 is such that if an increasing sequence x n → x ∈ A ¯ 0, then x n ≤ x, ∀n.

Since (C_{k}) is an increasing sequence, (lambda_{k}) is a decreasing sequence.

Let be the sequence defined by (1.15), where is a sequence in and is an increasing sequence in.

Let be a martingale-difference sequence and be an increasing sequence of positive numbers.

Let ({d_{i}}) be a sequence of variables adapted to an increasing sequence of σ-fields ({mathcal{F}_{i}}).