How to typeset the limit of a sequence like so?

Question

I want to write this:

I tried with $x_n \to_{n \to 0} 0$ but the $n \to 0$ doesn't go under the right arrow, it goes under but on the right, and I want it under but in the center, as in the picture above.

Answer 1

You can also use the function \xrightarrow:

$ x_n \xrightarrow[n \to 0]{} 0$

The user's guide of the amsmath package says :

\xleftarrow and \xrightarrow produce arrows that extend automatically to accommodate unusually wide subscripts or superscripts. These commands take one optional argument (the subscript) and one mandatory argument (the superscript, possibly empty)"

Answer 2

You can use the function of \underset and \overset, in this case an arrow is simply defined with:

\underset{n\to 0}{\longrightarrow}

Which points the expression related to "n" under the second argument, here there are two versions depending on the size of the underset (using \scriptscriptstyle):

\documentclass{article}
%
\usepackage{amsmath}
%
\begin{document}
%
\[
X_n\underset{n\to 0}{\longrightarrow}0 \qquad%
X_n\underset{\scriptscriptstyle{n\to 0}}{\longrightarrow}0
\]
%
\end{document}

Which yields:

Answer 3

If you wanted to change the depth of the underset below the arrow (for example, to 1 pt), then this could be done:

\documentclass{article}
\usepackage{stackengine}
\stackMath
\begin{document}
\( X_n  \mathrel{\stackunder[1pt]{\longrightarrow}{\scriptscriptstyle n \rightarrow 0}} 0 \)
\end{document}

Alternately, one could use something of Heiko's approach using \xrightarrow, but achieving a more snug fit like Fran's result, with the following:

\documentclass{article}
\usepackage{amsmath}
\usepackage{stackengine}
\stackMath
\begin{document}
$ x_n \mathrel{\stackunder[-7.5pt]{\xrightarrow[%
  \scriptscriptstyle\phantom{n \to 0}]{}}{\scriptscriptstyle n \to 0\,}} 0$
\end{document}

Finally, one could create the long arrow manually, and stack the underset below it:

\documentclass{article}
\usepackage{stackengine}
\stackMath
\begin{document}
\( X_n  \mathrel{\stackunder[-1pt]{-\mkern-5mu-\mkern-10mu\longrightarrow}{%
  \scriptscriptstyle n \rightarrow 0}} 0 \)
\end{document}

The one thing all three solutions have in common is they use stackengine to underset the subscript, which gives flexibility on the vertical location of the underset.

[Thanks to Qrrbrbirlbel for reminding me I forgot the \mathrel]

Answer 4

Here's a plain version:

$$ X_n \mathrel{\mathop{\kern0pt\longrightarrow}\limits_{n\to0}} 0 $$ \bye

which could be shortened like \buildrel with \def\relop#1#2{\mathrel{\mathop{\kern0pt #1}\limits_{#2}}} to be X_n \relop\longrightarrow{n\to0} 0.

Answer 5

$X_{n\overrightarrow{_{\;\;n\to0\;\;\;}}}0$

This is not as elegant as \xrightarrow, but like this command (and unlike \undersetmethod) the long arrow could longer (required for some wider than n \to 0). The difference with \xrightarrow is that (a) do not need the amsmath package, (b) long arrow could be also as shorter as the text under it, (c) a smaller arrowhead (d) produce a more compact formula. Bug or feature, depending of what you want. But in case of be regarded as a bug, the horizontal spacing can be solved adding some more spaces. The vertical spacing cab be solved following the Steven's answer. In this MWE the second formula have exactly the same horizontal spacing that using \xarrow.

\documentclass{article}
\begin{document}
$X_{n\overrightarrow{_{\;\;n\to0\;\;\;}}}0$

$X_{n\;\,\overrightarrow{_{\;n\to0\;\;\,}}}\;0$
\end{document}