# Why does lim_{n\to\infty} work in my LaTeX document?

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
@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}. –  yo' Mar 30 '12 at 7:07

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.

\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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