Non-increasing sequence

In mathematics a non-increasing sequence is a type sequence, an ordered list of objects, with an additional property on the values of its items. The property of being non-increasing is a local property in that if all adjacent items in the sequence have the property then the sequence over all has the property.

The property of being a decreasing sequence is a stronger requirement since any "decreasing sequence" is a "non-increasing sequence", but the converse is not true. A special example of a non-increasing sequence is the constant sequence where all items in the sequence have identical value.

Definition

Let "X" be a set, and "⊆" a partial order on "X". Let α be a sequence of ordinals. We say that a sequence of elements "x"α of "X" is non-increasing if for each ordinal α and each ordinal β>α, we have "x"β⊆"x"α.

Algebraically speaking, a sequence (a_n)_{n=1}^{infty} is non-increasing if forall ninmathbb N:a_ngeq a_{n+1}.

See also

*Monotonic function
*decreasing sequence


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Non-standard model of arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, …}. The elements… …   Wikipedia

  • Non-standard arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, hellip;}. The… …   Wikipedia

  • Non-rocket spacelaunch — Non rocket space launch (NRS) is a launch into space where some or all needed speed and altitude is provided by non rocket means, rather than simply using conventional chemical rockets from the ground. A number of alternatives to rockets have… …   Wikipedia

  • Non-volcanic passive margins — (NVPM) constitute one end member of the transitional crustal types that lie beneath passive continental margins; the other end member being volcanic passive margins (VPM). Transitional crust welds continental crust to oceanic crust along the… …   Wikipedia

  • Non-coding RNA — A non coding RNA (ncRNA) is a functional RNA molecule that is not translated into a protein. Less frequently used synonyms are non protein coding RNA (npcRNA), non messenger RNA (nmRNA) and functional RNA (fRNA). The term small RNA (sRNA) is… …   Wikipedia

  • Non-convexity (economics) — In economics, non convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences (that do not prefer extremes to in between values) and convex budget …   Wikipedia

  • Sequence (poetry) — This article is about Latin poems and songs. For the early music group, see Sequentia (music group) . For other uses, see sequence (disambiguation).A sequence (Latin: sequentia ) is a chant sung or recited during the Mass, before the proclamation …   Wikipedia

  • Long non-coding RNA — Long noncoding RNAs (long ncRNAs) are generally considered (somewhat arbitrarily) as non protein coding transcripts longer than 200 nucleotides. This limit is due to practical considerations including the separation of RNAs in common experimental …   Wikipedia

  • Main sequence — A Hertzsprung Russell diagram plots the actual brightness (or absolute magnitude) of a star against its color index (represented as B V). The main sequence is visible as a prominent diagonal band that runs from the upper left to the lower right.… …   Wikipedia

  • Multiple sequence alignment — A multiple sequence alignment (MSA) is a sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. In many cases, the input set of query sequences are assumed to have an evolutionary relationship by which they… …   Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.