# How to create well-aligned, clean structure to define a function (mathematics)?

I am new to Latex. I am aiming to define a function appropriately using latex, that is to first define the sets, e.g. $f:X \to Y$ and then how the elements map into the image, i.e. $x \to f(x)$. I would like both rows to align well. Below is the code and problem I encountered:

\begin{alignat*}{2}
X \colon T &\rightarrow {}&& \mathcal{D} \\
t&\mapsto \lim\limits_{n \to \infty}\sum_{\substack{i = 0,...,m}}(f(t_{i,n})-f(t_{i-1,n})\cdot(f(t_{i,n})-f(t_{i-1,n}))\\
\end{alignat*} I want the "D" to be just in line with the start of the limit in the "mapsto" row. Could anyone show me how to do this?

• Welcome! Use align (not alginat). \documentclass{article} \usepackage{amsmath} \begin{document} \begin{align*} X \colon T &\rightarrow \mathcal{D} \\ t&\mapsto \lim\limits_{n \to \infty} \sum_{\substack{i =0,\dots,m}} (f(t_{i,n})-f(t_{i-1,n})\cdot(f(t_{i,n})-f(t_{i-1,n})) \end{align*} \end{document}
– user194703
Mar 18 '20 at 19:53
• (Not tested.) @Schrödinger'scat has given a good suggestion. align is the way to go. I'm just going to verbally suggest adjustments. The && you used is what is shifting the \mathcal{D} way off to the right, so get rid of them. But since there is a limit on \lim, the "l" may be a bit to the right of the "D". Rather than trying to shift the \lim expression, if it's needed add a small space before the "D". \, should be more than enough; if it's too much, then \mspace{2mu} should work. (mu is a "math" unit, and a thin space = 3mu.) Mar 18 '20 at 20:04
• To explain what happened: the aligning environments line everything up on the & symbols. Since the first row has more & than the second, the extra & come after everything in the second row, and then the \mathcal{D} comes after that. Mar 19 '20 at 4:57

I want the \mathcal{D} to be just in line with the start of the limit in the \mapsto row.

I would use a top-aligned aligned (pun intended...) environment: \documentclass{article} % or some other suitable document class
\usepackage{mathtools}  % for "\smashoperator" macro
\begin{document}
X \colon \begin{aligned}[t] &T\rightarrow \mathcal{D} \\ &t\mapsto \lim_{n \to \infty} \smashoperator[r]{\sum_{i = 0,\dots,m}} (f(t_{i,n})-f(t_{i-1,n}))\cdot (f(t_{i,n})-f(t_{i-1,n})) \end{aligned}
\end{document}


Addendum: Here's a solution that implements @barbarabeeton's suggestion that the \rightarrow and \mapsto symbols should be aligned as well. \documentclass{article}
\usepackage{array,mathtools}
\begin{document}
$\setlength\arraycolsep{0pt} X \colon \begin{array}[t]{ r >{{}}c<{{}} >{\displaystyle}l } T &\rightarrow &\mathcal{D} \\[0.5ex] t & \mapsto & \smashoperator[l]{\lim_{n \to \infty}} \smashoperator[r]{\sum_{i = 0,\dots,m}} \bigl(f(t_{i,n})-f(t_{i-1,n})\bigr) \bigl(f(t_{i,n})-f(t_{i-1,n})\bigr) \end{array}$
\end{document}

• Nice, but really, the arrows should also be aligned. Mar 18 '20 at 20:09
• @barbarabeeton - That's not what the OP wrote (but I agree with you anyway!).
– Mico
Mar 18 '20 at 20:11
• Not what s/he wrote, but what it looks like in the visual. Mar 18 '20 at 20:13
• @barbarabeeton - Please see the addendum I just posted, with a solution that follows your guidelines.
– Mico
Mar 18 '20 at 20:20
• Yes. That does it. Mar 18 '20 at 20:41

Using Vincent's idea of an array, but with some more tricks to keep barbara beeton happy:

\documentclass{article}
\usepackage{amsmath,mathtools,calc}
\usepackage{array}

\begin{document}

$\begin{array}{ @{} r @{} c @{} >{\displaystyle{}}l @{} } X \colon{} & T & \to \mathop{\mathmakebox[\widthof{\lim}][l]{\mathcal{D}}}_{\hphantom{n\to\infty}} \\[1ex] & t & \mapsto \lim_{n \to \infty}\sum_{i=0,\dots,m} \mspace{-9mu} \bigl(f(t_{i,n})-f(t_{i-1,n})\bigr)\cdot\bigl(f(t_{i,n})-f(t_{i-1,n})\bigr) \end{array}$

\end{document} On the other hand, I'd simply do

We can define the map $X\colon T\to\mathcal{D}$ by
\begin{equation*}
X(t)=\lim_{n \to \infty}\sum_{i=0,\dots,m} \mspace{-9mu}
\bigl(f(t_{i,n})-f(t_{i-1,n})\bigr)\cdot\bigl(f(t_{i,n})-f(t_{i-1,n})\bigr)
\end{equation*} • +1 for the last advice! Mar 19 '20 at 14:57

After seeing the other answers... I really would like to reiterate my comment and use align here, with all the explanations being contained in barbara's comment (sorry, Mico ;-).

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{align*}
X \colon T &\rightarrow \mathcal{D} \\
t&\mapsto \lim\limits_{n \to \infty}
\sum_{\substack{i =0,\dots,m}}
(f(t_{i,n})-f(t_{i-1,n})\cdot(f(t_{i,n})-f(t_{i-1,n}))
\end{align*}

\emph{Maybe} one could use \verb|\mathclap| to align the $\mathcal{D}$ with
$\lim$ (but I am not coninced).
\begin{align*}
X \colon T &\rightarrow \mathcal{D} \\
t&\mapsto \lim\limits_{\mathclap{n \to \infty}}\;
\sum_{\substack{i =0,\dots,m}}
(f(t_{i,n})-f(t_{i-1,n})\cdot(f(t_{i,n})-f(t_{i-1,n}))
\end{align*}
Or, in the spirit of barbara beeton's comment.
\begin{align*}
X \colon T &\rightarrow\setbox0\hbox{$\lim\limits_{n \to \infty}$}%
\setbox1\hbox{$\lim$}%
\hspace{\the\dimexpr0.5\wd0-0.5\wd1}\mathcal{D} \\
t&\mapsto \lim\limits_{n \to \infty}\;
\sum_{\substack{i =0,\dots,m}}
(f(t_{i,n})-f(t_{i-1,n})\cdot(f(t_{i,n})-f(t_{i-1,n}))
\end{align*}
\end{document} • Looks good. Thanks. (I like the last example best; the gap after the "T" balances the space before the "D", even though that's largely a consequence of shape. To my eyes, the lower limit in the second example looks a bit squeezed next to the arrow.) Mar 18 '20 at 20:39
• @barbarabeeton I agree, which is why I wrote that I am not convinced about that one. Even the simpleminded align looks good IMHO,
– user194703
Mar 18 '20 at 20:44

I like to use the array environment for these definitions, since the syntax is rather visual.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
$\begin{array}{r@{\ }c@{\ }c@{\ }l} X \colon & T & \to & \mathcal{D} \\ & t & \mapsto & \displaystyle \smashoperator[l]{\lim_{n \to \infty}} \sum_{i=0,...,m} \bigl( f(t_{i,n})-f(t_{i-1,n})\cdot(f(t_{i,n})-f(t_{i-1,n}) \bigr) \end{array}$
\end{document} This way everything is aligned correctly. If the \lim_{n\to\infty} appears to be too close to the \mapsto symbol, some spacing could be added (for example with \,) before both the \mathcal{D} and the \lim_{n\to\infty} commands. Of course if this spacing is added but not on both lines, the alignment will be lost.

• This is technically correct, but the "D" isn't lined up with "lim", See my comment on the question. Mar 18 '20 at 20:08
• To line up the \mathcal{D} and lim particles, you could load the mathtools package and replace \lim_{n \to \infty} with \smashoperator[l]{\lim_{n \to \infty}}.
– Mico
Mar 18 '20 at 20:10
• Thank you both for your suggestions! I corrected the alignment of the \mathcal{D} and the \lim symbols. Mar 18 '20 at 20:19