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lim_ is not a command in LaTeX because all commands begin with a back slash.

However, why does lim_{n\to\infty} work in math mode? What is lim_ if it is not a command?

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just lim_ is treated as ordinary text and \lim_ is the maths way of using limits. –  Harish Kumar Mar 30 '12 at 0:51
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@HarishKumar I believe you are wrong. lim_ is not treated as an ordinary text. lim_ is standalone l, standalone i and standalone m with a following token as a subscript. To make it an ordinary text you have to put \mathit{lim}. –  tohecz Mar 30 '12 at 7:07
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1 Answer

up vote 16 down vote accepted

The macro for the limit operator is \lim.

Without the \, it just treated as three characters l, i, m. This is no different that $xy$ representing a product of two terms x, and y, so $lim$ is a product of three terms: l, i, m. So with $lim_{n\to\infty}$, the subscript is applied to the m term. Perhaps the meaning is more obvious if you write and equivalent statement:

$ l  i  m_{n\to\infty}$

Note that without the \ the three letters are in italics, representing variables. The operator \lim is not in italics representing an operator.

enter image description here

\documentclass[fleqn]{article}
\begin{document}
$lim_{n\to\infty}$

$\lim_{n\to\infty}$

\[ lim_{n\to\infty} \]
\[\lim_{n\to\infty} \]
\end{document}
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