# increasing sequence

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Related to increasing sequence: Decreasing sequence, Bounded sequence

## increasing sequence

[in¦krēs·iŋ ′sē·kwəns]
(mathematics)
A sequence of real numbers in which each term is greater than the preceding term.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
For pressures above 30 to 40 mmHg, the log-transformed median SWS values for the increasing sequence were higher than the ones for the decreasing sequence.
Sets [USI.sup.*] (I, S, [m.sub.0], [M.sub.0]) and [USI.sup.*.sub.u] (I, [S.sup.*], m, M) are well defined since the sequences S = [{[[zeta].sub.k]}.sup.[infinity].sub.k[greater than or equal to]0] and [S.sup.*] = [{[[zeta].sup.*.sub.k]}.sup.[infinity].sub.k[greater than or equal to]0] are strictly increasing sequences in I such that S [subset] [S.sup.*], [[zeta].sub.0] = a, [lim.sub.k[right arrow][infinity]] = b, and card of ([[zeta].sub.k], [[zeta].sub.k+1]) [intersection]([S.sup.*]\S) [less than or equal to] 1.
each permutation in D consisting of the skew sum of a sequence of plane trees, with an increasing sequence of points above (top points) and an increasing sequence of points to its left (left points).
In this case, there exists an increasing sequence ([K.sub.n]) [subset or equal to] K(X) with X = [[union].sup.[infinity].sub.n=1] [K.sub.n] satisfying the condition that each K in K(X) is contained in some [K.sub.n].
(2) Consider m [greater than or equal to] 2, m [member of] N*, times of geometric mean value operation by combining with Lemma 1 and (1/[2.sup.m]) < ((2 ln 3 - 3 ln 2)/(2 ln 2 - ln 3)) = 0.409..., and we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which is a monotone increasing sequence for each m.
(iv) Assume that there is a (in general, nonunique) strictly increasing sequence of nonnegative integers {[j.sub.k]} with [j.sub.0] = 0 and 0 < [j.sub.k + 1] - [j.sub.k] [less than or equal to] m < [infinity] such that
Since (X, Y) is a Runge pair of Stein spaces, there exists an increasing sequence of sets of the form [Z.sub.j] = {[[phi].sub.j] [less than or equal to] 0} [subset] Y such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [[phi].sup.j] : X [right arrow] R are possibly different real-analytic strictly psh exhaustion functions.
For this we need the concept of almost increasing sequence. A positive sequence ([b.sub.n]) is said to be almost increasing if there exists a positive increasing sequence ([c.sub.n]) and two positive constants A and B such that A[c.sub.n] [less than or equal to] [b.sub.n] [less than or equal to] B[c.sub.n] (see [1]).
Hence if n<m, we get [rho]([x.sup.(n)],0) < [rho]([x.sub.(m)],0) (1) Also, lim n [right arrow] [infinity] [rho]([x.sup.(n)],0)= [rho](x,0) and since [rho]([x.sup.(n)],0) is a monotonically increasing sequence, we get sup [rho]([x.sup.(n)],0) = [rho](x,0) (n) (2)
is of course an increasing sequence converging to e.
A positive sequence ([b.sub.n]) is said to be almost increasing if there exists a positive increasing sequence [c.sub.n] and two positive constants A and B such that A[c.sub.n] [less than or equal to] [b.sub.n] [less than or equal B[c.sub.n] (see [1]).
When Page and Neuringer removed these constraints, reinforcement contingent on sequence variability was effective at increasing sequence variability.

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