vertical position of \dots

Question

In this answer on math I wrote

$\frac 12=0.50000\dots =0.499999\dots $

The dots after the 50000 came out higher on the screen than the ones after the 499999. Changing it to \ldots works fine. Why are they higher with \dots in one case than another?

Answer 1

Observe that the issue you describe does not arise in a LaTeX document if the amsmath package is not loaded:

\documentclass{article}
\begin{document}
$\frac12=0.50000\dots=0.499999\dots$
\end{document}

Compare this output with what results if the amsmath package is, in fact, loaded:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
$\frac12=0.50000\dots=0.499999\dots$
\end{document}

The meanings of the two instances of \dots are quite evidently being interpreted differently. In the first instance, amsmath appears to judge that \cdots is appropriate (possibly because it thinks that there's a multiplicative relationship between 0.50000 and =), whereas it appears to judge that \ldots is appropriate in the second instance.

---

What to do -- if anything?

Quoting from section 4.3 of the user guide of the amsmath package:

For preferred placement of ellipsis dots (raised or on-line) in various contexts there is no general consensus. It may therefore be considered a matter of taste. By using the semantically oriented commands

• \dotsc for "dots with commas"
• \dotsb for "dots with binary operators/relations
• \dotsm for "multiplication dots"
• \dotsi for "dots with integrals"
• \dotso for "other dots" (none of the above)

instead of \ldots and \cdots, you make it possible for your document to be adapted to different conventions on the fly, in case (for example) you have to submit it to a publisher who insists on following house tradition in this respect.

Put differently, you have three choices -- assuming you're working with a LaTeX document and load the amsmath package:

• Use \dots and hope that your intended usage will coincide with how amsmath interprets the situation. Most of the time, this approach will work just fine.

• Use \ldots and \cdots ("lower dots" and "center dots") explicitly and don't give LaTeX and amsmath a chance to make decisions about the type of ellipsis to be used. The downside of this approach is that you may be misinterpreting what's optimal (or at least conventional) from a typographic standpoint.

• Use the "semantically oriented" \dots[x] commands instead of \dots. For the case at hand, you should probably be using \dotsc in both instances.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
$\frac12=0.50000\dotsc=0.499999\dotsc$
\end{document}