Sentence examples for is eventually decreasing from inspiring English sources

It follows from Lemma 3.2 that is eventually decreasing.

Case 1. Suppose that there exists some nonnegative integer m such that thesequence is eventually decreasing.

If { ∥ x n − z ∥ } n ∈ N is eventually decreasing, then there exists n 0 ∈ N such that the sequence { ∥ x n − z ∥ } n = n 0 ∞ is decreasing.

Since for we can find a constant such that for Then from (2.8) and the fact that is eventually decreasing, we have (29).

Case 1: ( s n ) is eventually decreasing (i.e. there exists k ≥ 0 such that s n > s n + 1 holds for all n ≥ k ).

Case 1. ( s n ) is eventually decreasing (i.e., there exists N ≥ 0 such that ( s n ) is decreasing for n ≥ N ).

It implies that x is eventually positive decreasing.

Applying Lemma 2.6 to (3.25), from the condition (i) we obtain s n → 0, that is, x n → p. Case 2: { s n } is not eventually decreasing, that is, we can find a positive integer n 0 such that s n 0 ≤ s n 0 + 1.

Applying Lemma 2.3 to (3.16), we obtain s n → 0. Case 2: ( s n ) is not eventually decreasing, that is, we can find an integer n 0 such that s n 0 ≤ s n 0 + 1.

From condition (ii) and Lemma 2.3, we obtain s n → 0. Case 2: { s n } is not eventually decreasing, that is, we can find a positive integer n 0 such that s n 0 ≤ s n 0 + 1.

and so is an eventually decreasing function.