“sequence”的概念、定义、翻译、参考文献-科学参考

sequence

Mathematics

A finite sequence consists of n terms a₁, a₂,…, a_n, in a given order, where n is the length of the sequence. An infinite sequence consists of terms a₁, a₂, a₃,…, one corresponding to each positive integer. Sometimes, it is more convenient to denote the terms of a sequence by a₀, a₁, a₂,…. Addition and scalar multiplication of sequences are defined componentwise, and so the set of sequences forms a vector space (see c, l^p). See also limit (of a sequence), series.

Computer

1. A function whose domain is the set of positive integers (or sometimes the set of nonnegative integers). The image set can thus be listed s₁,s₂,… where s_i is the value of the function given argument i. A finite sequence (or list) is a function whose domain is
${1, 2, \dots, n} for n \geq 1$
and hence whose image set can be listed
$s_{1}, s_{2}, \dots, s_{n}$
2. The listing of the image set of a sequence. Hence it is another name for string.

Logic

A generalization of the notion of a set in which elements are linearly ordered and may appear more than once, i.e., a tuple of elements. Sequences are important in sequent calculi, as some presentations of sequents assume that cedents—the sets of formulae appearing in a sequent—are sequences.

Philosophy

See ordered n-tuple.

单词	sequence
释义	sequence Mathematics A finite sequence consists of n terms a₁, a₂,…, a_n, in a given order, where n is the length of the sequence. An infinite sequence consists of terms a₁, a₂, a₃,…, one corresponding to each positive integer. Sometimes, it is more convenient to denote the terms of a sequence by a₀, a₁, a₂,…. Addition and scalar multiplication of sequences are defined componentwise, and so the set of sequences forms a vector space (see c, l^p). See also limit (of a sequence), series. Computer 1. A function whose domain is the set of positive integers (or sometimes the set of nonnegative integers). The image set can thus be listed s₁,s₂,… where s_i is the value of the function given argument i. A finite sequence (or list) is a function whose domain is ${1, 2, \dots, n} for n \geq 1$ and hence whose image set can be listed $s_{1}, s_{2}, \dots, s_{n}$ 2. The listing of the image set of a sequence. Hence it is another name for string. Logic A generalization of the notion of a set in which elements are linearly ordered and may appear more than once, i.e., a tuple of elements. Sequences are important in sequent calculi, as some presentations of sequents assume that cedents—the sets of formulae appearing in a sequent—are sequences. Philosophy See ordered n-tuple.
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