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":
... 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 ...
... 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 ... stop codon in combination with a downstream hairpin (SElenoCysteine Insertion Sequence, or SECIS) ... 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 ... of typicality 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 ...
... 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 ... 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 ...
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 isnt 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 historys 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 formit may be called fleeting or eternalis in neither case the stuff that life is made of.”
—Walter Benjamin (18921940)