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
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)