Sentence examples for strictly decreasing sequence from inspiring English sources

Let be a strictly decreasing sequence in.

where is a strictly decreasing sequence in and set.

Let and assume that is a strictly decreasing sequence.

Since is a strictly decreasing sequence and, we have.

Let with be a strictly decreasing sequence, and with.

We can choose so that there exists a strictly decreasing sequence such that  .

where is defined by (3.8) and is a strictly decreasing sequence in.

The conditions (3.18) and (3.19) lead to strictly increasing and strictly decreasing sequences of the solution of finite sizes n i ∈ N, i ∈ N 0, respectively.

Set f ( x ) = T n 1 ( x ) − β 2. Note that f < 0 and f ( β 2 ) > 0. By the monotonicity of f ( x ), we know that there exists a unique point β 3 ∈ ( α, β 2 ) such that T n 1 ( β 3 ) = β 2. Proceeding like this, we can obtain a strictly monotone decreasing sequence { β m } ⊂ , which satisfies T n 1 ( β m + 1 ) = β m ( m = 2, 3, … ).

So, if Algorithm 3 does not converge, we will find an infinite strictly decreasing integer sequence r 1>r 2>r 3>⋯.

That is, ({sigma_{b}(x_{n},x_{n+1})}) is a strictly decreasing positive sequence in (mathbb{R}^) and it converges to some (rgeq0).