# ascending sequence

## ascending sequence

[ə‚sen·diŋ ′sē·kwəns]
(mathematics)
A sequence of elements of a partially ordered set such that each member of the sequence is equal to or less than the following one.
In particular, a sequence of sets such that each member of the sequence is a subset of the following one.
References in periodicals archive ?
b04) each ascending sequence in Dom([phi]) has an upper bound (in M).
We have thus constructed an ascending sequence ([u.
Art Connoisseur seems to be progressing in a similar fashion to his sire Lucky Story, who produced an ascending sequence of Racing Post Ratings on his five starts at two, culminating in a 117 in the Group 2 Champagne Stakes, and it is possible that Art Connoisseur, who has shown marked improvement on each of his three starts to post RPRs of 83, 99 and 113, will be able to challenge the 120 RPR barrier next time we see him.
In a seminal 1943 paper, he divided human needs into broad groups and arranged them in an ascending sequence.
The auctioneer can just as well cry out an ascending sequence of prices to the gathered bidders, stopping the auction when enough are willing to take down the total issue.
A serial master file contains customer name and address records, arranged in ascending sequence by customer number.
each ascending sequence has an upper bound (modulo ([less than or equal to]))
Further, call the quasi-order ([less than or equal to]), self-closed provided M(x, [less than or equal to]) := {u [member of] M; x [less than or equal to] u} is ([less than or equal to])-closed, for each x [member of] M; or, equivalently: the limit of each ascending sequence is an upper bound of it (modulo ([less than or equal to])).

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