# \dots=\bot behaves in mathtools/amsmath differently than in pure LaTeX

Consider the following input:

\documentclass{standalone}
\usepackage{mathtools}%%% culprit. Same with amsmath
\begin{document}
The formulas of the form $$\dots=\bot$$ and $$\bot=\dots$$ can be simplified to $$\neg\mathrm{defined}(\dots)$$.
\end{document}


As we all know, the equality is commutative:

In particular, the first ellipsis is vertically centered, whereas the second is on the baseline. Why? Who on earth in his or her sane mind would render them differently depending on the side of the equation? Without mathtools (and without amsmath), both occurrences are lowered. I don't care that much about which variant is used, but I do care than the first two ellipses in the example look the same, since they mean the same thing. Which variant is the typographically more pleasant to read with equality? The documentation of amsmath (amsldoc) does not mention the equality sign, so I would think of \dotsb and \dotso. Which one(s) are to be used in the above context and why?

• it is not mathtools but amsmath. Check the documentation (amsldoc.pdf) for the various \dots commands. – Ulrike Fischer Sep 4 '18 at 19:21
• @UlrikeFischer are you meaning to say that the \dots command is supposed to render two different types of dots based on whether there is an = sign?! – Andreas Storvik Strauman Sep 4 '18 at 19:22
• @AndreasStorvikStrauman yes. – Ulrike Fischer Sep 4 '18 at 19:23
• @UlrikeFischer Huh. I guess it kinda makes sense. Considering X=(1,\dots,n) and a=b=\dots=z you'd want different dots... – Andreas Storvik Strauman Sep 4 '18 at 19:26
• You can use \ldots or \cdots to get one or the other. – Skillmon Sep 4 '18 at 19:26

Define \lellipsis as you prefer and use it:

\documentclass{article}
\usepackage{geometry} % just to avoid an overfull box in the example
\usepackage{amsmath}

\newcommand{\lellipsis}{{\cdots}}

\begin{document}

The formulas of the form $$\lellipsis=\bot$$ and $$\bot=\lellipsis$$
can be simplified to $$\neg\operatorname{defined}(\lellipsis)$$.

\end{document}


The reason for the asymmetry is that, with amsmath, \dots looks for what follows, in order to print the most desirable kind of dots (low or centered) depending on the context. In your case you want to be independent of context and also to make the symbol ordinary, rather than punctuation, hence the additional braces.

• @user49915 Exactly; I wouldn't use dots myself, but rather a metavariable. – egreg Sep 4 '18 at 22:42