Placement of ellipsis

Question

Consider the following example:

\documentclass{article}
\begin{document}
$(1-\theta_1) \dots (1-\theta_m)$
\end{document}

Isn't the ellipsis supposed to be vertically centered since they indicate multiplication?

Update

I'm now fully convinced that I'm wrong. To everyone with access to The TeXbook, have a look at page 172. :)

Answer 1

In the base LaTeX format \dots is just an alias for \ldots and is always on the baseline.

If you add amsmath then it does change according to context, but not in this case, it is more optimised for the case where the binary operator is explicit:

\documentclass{article}
%\usepackage{amsmath}
\begin{document}
$(1-\theta_1) \times \dots \times(1-\theta_m)$
\end{document}

The dots will raise if you uncomment amsmath.

Answer 2

Only for the best practitioners. We should stick to the semantic rules by using the following dots.

\documentclass[preview,border=12pt]{standalone}
\usepackage{amsmath}
\begin{document}
\begin{itemize}
    \item \verb+\dotsc+ for comma separated element $A_1, A_2, \dotsc, A_{n-1}, A_n$.
    \item \verb+\dotsb+ for binary operator $A_1 +A_2 + \dotsb + A_{n-1} + A_n$.
    \item \verb+\dotsm+ for multiplication $A_1 A_2 \dotsm A_{n-1}  A_n$.
    \item \verb+\dotsi+ for integral  $\int_{A_1} \int_{A_2} \dotsi \int_{A_{n-1}}  \int_{A_n}$.
    \item \verb+\dotso+ for others.
\end{itemize}
\end{document}

Advantages:

You can redefine the implementation for each dots above in the preamble whenever your institution ask you to change its behavior to meet its own adopted layout. If you use just \ldots and \cdots rather than the above semantic dots then you have to manually change them per equation --- as a result, this job makes your life boring.

\dots (general dots) versus \dots* (amsmath's semantically defined dots)

\documentclass[preview,border=12pt,varwidth]{standalone}
\usepackage{amsmath,xcolor}
\begin{document}
\begin{itemize}
        \item (\verb+\dots+)  $A_1, \dots, A_n$ \textcolor{red}{v.s.}\ $A_1, \dotsc, A_n$  (\verb+\dotsc+).
    \item (\verb+\dots+)  $A_1 + \dots + A_n$ \textcolor{red}{v.s.}\ $A_1 + \dotsb + A_n$ (\verb+\dotsb+).
    \item (\verb+\dots+)  $A_1 \dots  A_n$ \textcolor{red}{v.s.}\ $A_1 \dotsm  A_n$ (\verb+\dotsm+).
    \item (\verb+\dots+) $\int_{A_1} \dots  \int_{A_n}$ \textcolor{red}{v.s.}\ $\int_{A_1} \dotsi  \int_{A_n}$ (\verb+\dotsi+).
    \item (\verb+\dots+) \dots\ \textcolor{red}{v.s.}\ \dotso\ (\verb+\dotso+).
\end{itemize}
\end{document}