Sequence

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 "sequences, sequence":

Typical Set
... 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 ... it provides a theoretical means for compressing data, allowing us to represent any sequence Xn using nH(X) bits on average, and, hence, justifying the use ...
Farey 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 ... 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 ...
Translation (biology) - Genetic Code
... 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 ... combination with a downstream hairpin (SElenoCysteine Insertion Sequence, or SECIS) ... computer programs capable of translating a DNA/RNA sequence into a protein sequence ...
Y2H - Applications - Zinc Finger Protein Selection
... protein used in the construction of custom DNA-binding domains that bind to a desired DNA sequence ... 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 interaction with the ... ZFP is engineered into a 'scaffold' consisting of another two ZFPs of constant sequence ...
Lebesgue's Monotone Convergence Theorem - Theorem
... 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 ...

Famous quotes containing the word sequence:

    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)