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In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and the exact same elements can appear multiple times at different positions in the sequence.

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Wikipedia about sequence

In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and the exact same elements can appear multiple times at different positions in the sequence.

For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers (2, 4, 6,...).

Cauchy%20sequence%20illustration2.png

Examples and notation

There are various and quite different notions of sequences in mathematics, some of which (e.g., exact sequence) are not covered by the notations introduced below.

A sequence may be denoted (a1, a2, ...). For shortness, the notation (an) is also used.

A more formal definition of a finite sequence with terms in a set S is a function from {1, 2, ..., n} to S for some n ≥ 0. An infinite sequence in S is a function from {1, 2, ...} (the set of natural numbers without 0) to S.

Sequences may also start from 0, so the first term in the sequence is then a0.

A sequence of a fixed-length n is also called an n-tuple. Finite sequences include the empty sequence ( ) that has no elements.

A function from all integers into a set is sometimes called a bi-infinite sequence, since it may be thought of as a sequence indexed by negative integers grafted onto a sequence indexed by positive integers.

Types and properties of sequences

A subsequence of a given sequence is a sequence formed from the given sequence by deleting some of the elements without disturbing the relative positions of the remaining elements.

If the terms of the sequence are a subset of an ordered set, then a monotonically increasing sequence is one for which each term is greater than or equal to the term before it; if each term is strictly greater than the one preceding it, the sequence is called strictly monotonically increasing. A monotonically decreasing sequence is defined similarly. Any sequence fulfilling the monotonicity property is called monotonic or monotone. This is a special case of the more general notion of monotonic function.

The terms non-decreasing and non-increasing are used in order to avoid any possible confusion with strictly increasing and strictly decreasing, respectively. If the terms of a sequence are integers, then the sequence is an integer sequence. If the terms of a sequence are polynomials, then the sequence is a polynomial sequence.

Search results for Sequence

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sequence: Definition from Answers.com

Se·quence n. (s ē 'kw e ns) [F. séquence , L. sequentia , fr. sequens . See Sequent. ... example, (C, R, Y) is a sequence of letters that differs from (Y, C, ...www.answers.com/topic/sequence-4

Sequence

A Sequence is a variable-sized Container whose elements are arranged in a strict ... Creates a sequence with n elements initialized to a default value. ...www.sgi.com/tech/stl/Sequence.html

sequencehair.com

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sequence - Definition from the Merriam-Webster Online Dictionary

Definition of sequence from the Merriam-Webster Online Dictionary with audio pronunciations, thesaurus, Word of the Day, and word games.www.merriam-webster.com/dictionary/sequence

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News about Sequence

Gertrude’s Secret

EDP24 - Eastern Daily PressPlaygoers in Norwich on Saturday were able to spend an evening in the company of - among others - a past-it South African fitness instructor; a wannabe sex shop entrepreneur and a bitter ex-docker, all of whom feature in this sequence of monologues by Benedick West.http://www.edp24.co.uk/content/WhatsOn/story.asp?brand=EDPOn...

Cyanobacterium sequenced features rare linear chromosome

EurekAlert!( Washington University in St. Louis ) A team of researchers headed by biologists at Washington University in St. Louis has sequenced the genome of a unique bacterium that manages two disparate operations -- photosynthesis and nitrogen fixation -- in one little cell during two distinct cycles daily. Himadri. Pakrasi, WUSTL professor of biology, spearheaded the drive to sequence the genome of ...http://www.eurekalert.org/pub_releases/2008-09/wuis-csf09120...

Dragon Quest IV: Chapters of the Chosen (ds: 2008): Reviews

metacriticStars indicate the most critically-acclaimed games. A tale of epic proportions told through a unique chapter sequence that enables players to experience multiple character perspectives.http://www.metacritic.com/games/platforms/ds/dragonquest4cha...

John McCain campaign tries to quell 'Troopergate'

AP via Yahoo! News The presidential campaign of Sen. John McCain is trying to put to rest the ethical controversy that's come to be known as "Troopergate," releasing e-mails supporting Alaska Gov. Sarah Palin's contention that she dismissed her public safety commissioner over budget disagreements, not because he wouldn't fire her ex-brother-in-law.http://news.yahoo.com/s/ap/20080916/ap_on_el_pr/palin_troope...

SOA deployments: What actually works

InfoWorld via Yahoo! News SOA may have seemed the savior of bad software architecture and poor development project planning, but the reality is that it's a complex and difficult venture. Thus, the number of failed SOA projects is about equal to the successful ones. In other words, you have a 50 percent chance of failing, and the odds of failure are even greater if you work within a larger Global 2000 organization or ...http://news.yahoo.com/s/infoworld/20080916/tc_infoworld/1111...

News about Sequence

Sequence screen capture app adds sound recording

Mac CentralApp4mac has released Sequence 1.1, an update for their screen capture utility for Mac OS X. A free update for registered users, Sequence costs $29. Sequence lets you capture individual screenshots as well as video of your Mac. The software leverages ... http://www.macworld.com/article/135916/2008/10/sequence.html...

Oasis Scores Seventh Straight U.K. No. 1

BillboardAlso bouncing back was Ne-Yo's "Miss Independent" (Def Jam), which after falling 9-11 last week, improved to No. 6, and "Cookie Jar" (Decaydance/Fueled By Ramen) by Gym Class Heroes featuring the-Dream, which has a three-week sequence of 6-10-9. The ... http://www.billboard.com/bbcom/news/article_display.jsp?vnu_...

Swing Sequence: Vijay Singh

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Indiana Jones leads impressive list of new Blu-ray releases

Modesto BeePay close attention to the opening sequence in a huge warehouse. During the chase inside, one of the big crates is accidentally cracked open. The characters don't notice it, but inside the case is the Lost Ark, which has been stored there for nearly ... http://www.modbee.com/2041/story/461638.html

The Cheapest Genome Sequence Ever: For Real?

WiredThis story has been updated. A biotech startup company promises to decipher the human genome for $5,000 -- a price tag that could literally change the world, making high-resolution genetic scans available to relatively low-budget laboratories, and ... http://blog.wired.com/wiredscience/2008/10/the-cheapest-ge.h...

Search results for Sequence

Sequence (board game) - Wikipedia, the free encyclopedia

Sequence is a board-and-card game distributed by jax Ltd., Inc.. It involves an average-sized playing board, on which are depicted two decks of cards (minus the Jokers and Jacks ... http://en.wikipedia.org/wiki/Sequence_%28board_game%29

Welcome to the Sequence web site

Sequence is a national network of estate agents, with over 320 offices operating under 11 well known local names. We handle tens of thousands of moves for people all over the ... http://www.sequencehome.co.uk/

Sequence -- from Wolfram MathWorld

A sequence is an ordered set of mathematical objects. Sequences of object are most commonly denoted using braces. For example, the symbol {2n}_(n=1)^infty denotes the infinite ... http://mathworld.wolfram.com/Sequence.html

Amazon.com: Sequence Game: Toys & Games

Amazon.com: Sequence Game: Toys & Games ... Save $5 when you spend $25 and pay with Bill Me Later®. Offer valid Sept 1, 2008 - Sept 30, 2008.http://www.amazon.com/Jax-8002-Sequence-Game/dp/B00000IVAK

Sequence - leading digital agency based in Cardiff

Sequence is a leading digital agency in the UK. Whether it's a corporate website, an e-commerce platform, a staff intranet or a digital marketing campaign, Sequence can deliver the ... http://www.sequence.co.uk/
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Videos found for Sequence

Sequence 01

Sequence 01SwallowfieldFlash - Video

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'Kung Fu Panda' Exclusive Video: Opening Dream SequenceIn this animated family comedy, jungle animals threatened by a gang of snow leopards call on an inept panda to becoming a kung fu master and save the Valley of Peace. Vocal stars...Windows Media - Video

WEB EXTRA: Inmates Perform 'Thrille...

WEB EXTRA: Inmates Perform 'Thriller' Dance SequenceWEB EXTRA: Inmates Perform 'Thriller' Dance SequenceWindows Media - Video

Sequence of events

Sequence of eventsCNN's Susan Candiotti has new details on the sequence of events in Anna Nicole Smith's death. (February 9)Windows Media - Video

Deep Purple: Drifter Rehearsal Sequ...

Deep Purple: Drifter Rehearsal SequenceFrom the album Days May Come and Days May GoVideo - Video

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roma_sequence1.mpg

roma_sequence1.mpgTexte rédigé par Laurent Scotto Séquences du film à visionner : Séquence Maggiore/Questore Séquence La panetteria mpeg: 27.0 MB w:384px - h:288px

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Sequence - BrizOliEdit3.mpeg

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Answers for Sequence

Jeffrey K

Is every possible sequence of digits somewhere is the number pi?

Jeffrey KI think that such a possibility would defeat the purpose of irrationality. If it could be proven when, where, or if a sequence exists, then pi becomes more predictable. With greater analysis over a ...
Normand J

How do I sort my stock portfolios in a different sequence than they are now sorted?

Normand JOn Yahoo Finance, My portfolio select the portfolio you want. In the top left corner of the screen there should be button labeled "create/edit portfolio." Click it to go to the edit screen. Under ...
Michael C

What purpose does the Fibonacci sequence serve?

Michael Cthere are a lot of applications of that Fibonacci sequence in mathematics, one of my favorites is the binomial theorem, the pascal's triangle in which that sequence is related. It's hard to enumerate ...
Sweetness and Light

Writers, do you have problems establishing a natural sequence of your ideas when writing?

Sweetness and LightNo, not really. Maybe this is your style coming out unself-consciuousely?
beamer26

If given a sequence of nucleotides, how can you tell if it is regulated?

beamer26You cannot just look at a nucleotide sequence and say whether it regulates something. You need to know where this sequence is located relatively to the gene of interest. If you are looking at a sequ...

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