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":

... protein used in the construction 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 host a DNA-ZFP ... engineered into a 'scaffold' consisting of another two ZFPs of constant

**sequence**...

**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 ... 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 ...

... 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 ... is only concerned with the probability of a

**sequence**and not the actual

**sequence**itself ... theoretical means for compressing 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 ...

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

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

**sequence**with ... by a conventional 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**...

... Let be a pointwise non-decreasing

**sequence**of -valued Σ–measurable functions, i.e ... 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 ...

### Famous quotes containing the word sequence:

“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)

“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)