Sequence

In mathematics, a sequence is an infinite list x₁, x₂, x₃, ... (Sometimes finite lists are also called sequences, but not in the mathematical part of this article.)

Formally, a sequence can be defined as a function from N (the set of natural numbers, usually excluding 0) into some set S.

If S is the set of integers, then the sequence is an integer sequence.

If S is endowed with a topology then it is possible to talk about convergence of the sequence. A sequence converges to a limit x if every open set containing x also contains all but finitely many of the terms of the sequence. For example, the sequence of real numbers ¹/₂, ¹/₃, ¹/₄, ¹/₅, ... converges to 0. In general, it is possible for a sequence to converge to more than one limit, but this cannot happen in a Hausdorff space. A sequence that does not converge to any point is said to diverge.

See also Infinite Series.

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In biochemistry, sequence refers to a string of monomers that constitute a biopolymer.

The convention for a protein is to list its constituent amino acid residues as they occur from the amino terminus to the carboxylic acid terminus.

The convention for a nucleic acid sequence is to list the nucleotides as they occur from the 5' end to the 3' end of the polymer chain, where 5' and 3' refer to the numbering of carbons around the ribose? ring which participate in forming the phosphate diester linkages of the chain.

There are a number of biophysical techniques for determining sequence information. Protein sequence can be determined by [Edman degradation]?, in which the N-terminal residues are hydrolyzed from the chain one at a time, derivatized, and then identified. [Mass spectrometric]? techniques can also be used. Nucleic acid sequence can be determined using gel electrophoresis and capillary electrophoresis.

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