# decreasing sequence

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Related to decreasing sequence: Increasing sequence

## decreasing sequence

[di¦krēs·iŋ ′sē·kwəns]
(mathematics)
A sequence of real numbers in which each term is less than the preceding term.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Linear regression plots were also created for every region and direction (increasing versus decreasing sequence) of measurement, in order to obtain better knowledge of the dataset for the following modeling.
We have that {g([a.sub.n])} is a strictly decreasing sequence in [sigma](z).
which implies that [mathematical expression not reproducible] is decreasing sequence in [0, [infinity]) and hence it is convergent.
Decreasing sequences of rectangles are defined analogously.
According to step 5, if decreasing sequence (l) of a channel is greater than or equals to the [l.sub.0], it will proceed to step 6, i.e., the switching metric module.
Both [s.sub.n] = [(1 + (1/n)).sup.n+[alpha]] and [t.sub.n] = [(1 + (1/n)).sup.n+1] (1 + ([alpha]/n)) are monotone decreasing sequences if and only if [alpha] [greater than or equal to] (1/2).
 D.M.Hyman, On decreasing sequences of compact absolute retracts, Fund.
Therefore, {d([f.sup.n]z, x)} is a monotone decreasing sequence. Following the lemma 2.2, it can be proved that there exists a q [member of] int P [union] {0} such that
(iii) For every decreasing sequence [([U.sub.n]).sub.n] of clopen subsets of X there is an m [member of] N such that [U.sub.n] = [U.sub.m] for all n [greater than or equal to] m.
Since (x,y) [member of] [X.sub.[less than or equal to]], (Tx,Ty) [member of] [X.sub.[less than or equal to]] and so {d([T.sup.2n]x, [T.sup.2n]y)} is a decreasing sequence and d([T.sup.2n]x, [T.sup.2n]y) [down arrow] d([x.sup.*], [Tx.sup.*]).
The second set of conditions is given via a decreasing sequence of codistributions of differential one-forms .

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