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

For example, (M, A, R, Y) is a sequence of letters that differs from (A, R, M, Y), as the ordering matters, and (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be *finite*, as in this example, or *infinite*, such as the sequence of all even positive integers (2, 4, 6,...). Finite sequences are sometimes known as *strings* or *words* and infinite sequences as *streams*. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.

Read more about Sequence: Examples and Notation, Types and Properties, Analysis, Series, Infinite Sequences in Theoretical Computer Science, Vectors, Doubly Infinite Sequences, Ordinal-indexed Sequence, Sequences and Automata

### Other articles related to "sequence, sequences":

**Sequence**

... In mathematics, the Farey

**sequence**of order n is the

**sequence**of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to n, arranged in order of increasing size ... Each Farey

**sequence**starts with the value 0, denoted by the fraction 0⁄1, and ends with the value 1, denoted by the fraction 1⁄1 (although some authors omit these terms) ... A Farey

**sequence**is sometimes called a Farey series, which is not strictly correct, because the terms are not summed ...

... Let be a pointwise non-decreasing

**sequence**of -valued Σ–measurable functions, i.e ... for every k ≥ 1 and every x in X, Next, set the pointwise limit of the

**sequence**to be f ... If the

**sequence**satisfies the assumptions μ–almost everywhere, one can find a set N ∈ Σ with μ(N) = 0 such that the

**sequence**is non-decreasing for every ...

... of custom DNA-binding domains that bind to a desired DNA

**sequence**... By using a selection gene with the desired target

**sequence**included in the UAS, and randomising the relevant amino acid

**sequences**to produce a ZFP library, cells that ... 'scaffold' consisting of another two ZFPs of constant

**sequence**...

... can only be predicted using sophisticated algorithms, the amino acid

**sequence**, called primary structure, can be determined solely from the nucleic acid

**sequence**with the aid of a translation table ... stop codon in combination with a downstream hairpin (SElenoCysteine Insertion

**Sequence**, or SECIS) ... There are many computer programs capable of translating a DNA/RNA

**sequence**into a protein

**sequence**...

... In information theory, the typical set is a set of

**sequences**whose probability is close to two raised to the negative power of the entropy of their source distribution ... is only concerned with the probability of a

**sequence**and not the actual

**sequence**itself ... data, allowing us to represent any

**sequence**Xn using nH(X) bits on average, and, hence, justifying the use of entropy as a measure of information from a source ...

### Famous quotes containing the word sequence:

“It isn’t that you subordinate your ideas to the force of the facts in autobiography but that you construct a *sequence* of stories to bind up the facts with a persuasive hypothesis that unravels your history’s meaning.”

—Philip Roth (b. 1933)

“Reminiscences, even extensive ones, do not always amount to an autobiography.... For autobiography has to do with time, with *sequence* and what makes up the continuous flow of life. Here, I am talking of a space, of moments and discontinuities. For even if months and years appear here, it is in the form they have in the moment of recollection. This strange form—it may be called fleeting or eternal—is in neither case the stuff that life is made of.”

—Walter Benjamin (1892–1940)

“We have defined a story as a narrative of events arranged in their time-*sequence*. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time *sequence* is preserved, but the sense of causality overshadows it.”

—E.M. (Edward Morgan)