68N15-Iterator.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{Iterator}
\pmcreated{2013-03-22 16:25:16}
\pmmodified{2013-03-22 16:25:16}
\pmowner{PrimeFan}{13766}
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\pmtitle{iterator}
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\pmprivacy{1}
\pmauthor{PrimeFan}{13766}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{68N15}

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\begin{document}
An \emph{iterator} is a variable that one by one takes on all the values (usually integers) in a given range. The letter $i$ is often used for iterators (though that letter is overloaded as the imaginary unit), $j$ is often used as a second iterator.

In mathematics iterators are most often used in sum and product notation. For example, in $$\prod_{i = 3}^7 42i^2$$ the iterator $i$ takes on values from 3 to 7.

In computer programming languages iterators are often associated with the "for" reserved word, e.g., ``\verb!FOR I = 1 TO 47!'' in BASIC, ``\verb!for (i = 1; i < 48; i++)!'' in C++. In Mathematica, iterators are often given in curly braces together with an (omittable) initial value and a required finish value separated by commas, e.g., ``\verb=Table[2^n - 1, {n, 2, 48}]=''.
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