What is the difference between \ldots and \cdots?
For example, To write a sequence of points which is best to use?
a_1,\ldots,a_n Or a_1,\cdots,a_n.
Couple of examples of the difference can be useful.
[Tex/LaTex] the difference between \ldots and \cdots
amsmath
Related Solutions
The star at the end of the name of a displayed math environment causes that the formula lines won't be numbered. Otherwise they would automatically get a number.
You can read about that in the amsmath user's guide since align belongs to amsmath.
Such information can usually be found in the package documentation. Type texdoc packagename at the command prompt or visit http://ctan.org/pkg/packagename. If you use google or another search engine, look for starred and commandname.
Commonly, a star symbol * means a version of a command that behaves differently from the original. That often means suppressing numbering but could also refer to special features. For example, have a look at What's the difference between \newcommand and \newcommand*?
There are many differences. The main one is in the fact that \mathrm{xyz} behaves like an ordinary letter, while \operatorname{xyz} behaves like function names such as \sin. Here's an illustration
$\sin x + \sin(x+y) + a\sin z$
$\mathrm{sin} x + \mathrm{sin}(x+y) + a\mathrm{sin}z$
where it's clear that the second line is typeset wrong. Even if your "operator" requires parentheses after it, it should be \operatorname, as the third summand shows, where a thin space separates the coefficient from the operator.
Another subtle difference is in how some characters are interpreted in \mathrm and in \operatorname. Suppose you have an operator to be called "pre-norm", with a hyphen. Here's the example
$\operatorname{pre-norm}(\mathbf{v})$
$\mathrm{pre-norm}(\mathbf{v})$
and now it's clear what is to be used. Indeed \operatorname (and the same holds for macros defined with \DeclareMathOperator) treats punctuation symbols in a special way; \mathrm, instead, treats them as math symbols.
Best Answer
Although I agree with egreg's comment, the difference is mainly of an aesthetic nature imo. It depends on the context which version to use, which is also how
amsmathdecides which to use.Some examples:
a_1,\ldots,a_naligns better thana_1,\cdots,a_n.But
a_1 \to \ldots \to a_naligns worse thana_1 \to \cdots \to a_n.The alignment chosen by amsmath is usually the one commonly found in mathematical articles. However, I guess its not really wrong or anything to deviate from it.