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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
@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
up vote 23 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



\[ lim_{n\to\infty} \]
\[\lim_{n\to\infty} \]
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enter image description here

$\lim_{a\to b}$

In Textmode $\lim\limits_{a\to b} \frac{a}{b}$ or \\

in Displaymode $\displaystyle \lim_{a\to b} \frac{a}{b}%
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Did you notice the answer tex.stackexchange.com/a/50029/14757 above? Why you wrote such simpler answer? – Sigur Jan 21 at 15:12

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