Difference of the \dots*

Question

I came to wonder, what is the difference between the following?

\dotsc
\dotso

As well as between:

\dotsb
\dotsi
\dotsm

Answer 1

The following is taken directly from the amsmath documentation (section 4.3 Dots, p 11):

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. The default treatment for the various kinds follows American Mathematical Society conventions:

How is it "possible for your document to be adapted to different conventions on the fly"? Well, if you exercise consistent macro usage across the various document elements, a "house tradition" different from the current definition could be employed by using a redefinition. See, for example, the suggestion contained within Consistent typography.

At face value, and purely for comparison reasons, here's a take on x,\dots*,y:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\verb|\dots |: $x,\dots,y$ \par
\verb|\dotsc|: $x,\dotsc,y$ \par
\verb|\dotso|: $x,\dotso,y$ \par
\verb|\dotsb|: $x,\dotsb,y$ \par
\verb|\dotsi|: $x,\dotsi,y$ \par
\verb|\dotsm|: $x,\dotsm,y$
\end{document}

Answer 2

amsmath redefines \dots so that it can do a lookahead in order to establish what kind of dots to use. So, in general, just \dots is to be used and in-house styles just need to redefine internal macros to adapt the typescript output to different conventions.

However, for the cases when the kind of dots can't be desumed from the context, amsmath provides other ‘semantically oriented’ macros:

• \dotsc (dots with commas)
• \dotsb (dots for binary operations or relations, excluding multiplication)
• \dotsm (dots for multiplication)
• \dotsi (dots for integrals)
• \dotso (none of the above)

So you'll type

$(v_{1},v_{2},\dots,v_{n})$

and the dots will be set according to the style (default, the AMS in-house style). If you have an infinite array, instead, type

$(v_{1},v_{2},\dots,v_{n},\dotsc)$

so the trailing dots will be the same as the middle ones. Similarly, a finite sum will be

$a_{1}+a_{2}+\dots+a_{n}$

while an infinite sum will be

$a_{1}+a_{2}+\dots+a_{n}+\dotsb$

There's a different type for multiplication, because in some styles (AMS, for instance) the dots used for additions or equality are different from those used for multiplication (centered in the former case, low in the latter).

Do you see why? In the infinite array case the dots are followed by ), so making it impossible to know what kind of dots to use; in the infinite sum cases the formula ends and the situation is similar. Thus you have to help LaTeX, suggesting it the context.

Usage of these commands should be reserved to such cases; in general \dots suffices and it will do the right choice. Don't use \ldots or \cdots with amsmath: the ‘abstract’ version \dots works in the vast majority of cases, with the exception of those outlined above.