What to do about \ldots in lists and ending a sentence?

Consider the following

\documentclass{article}
\begin{document}
Let $X_1, X_2, \ldots$ be IID random variables.
We also consider an independent set of coin flips $Y_1, Y_2,\ldots$.
\end{document}

Two things are at issue here:

• Is the first use of \ldots the "proper" way to give a suggested list? Or should I do something like $X_1$, $X_2$, $\ldots$? Or is \ldots even appropriate at all?

• Same question for the second use case. Do I put a period at the end of the sentence, or does that last dot in the \ldots count? Or should ending a sentence with ellipses be avoided?

• I would do the same as you. – Sigur May 16 '17 at 22:50

I don't think it matters much but as a general rule I'd say that if the commas are part of the formal mathematical construct (because you are constructing some mathematical list or set) you should have the , in the math, but if it is an informal list and the commas are part of the sentence structure, have them outside the math.

Here with ellipsis, it's tending towards the informal sentence structure (but even that isn't a definite yes/no decision), so I'd probably use the second form in the example below. I've also used a final full stop after the ellipsis as that seems to be the logical thing to do, but four in a row looks a bit long and I wouldn't argue if an editor said to drop that.

\documentclass{article}
\begin{document}
Let $X_1, X_2, \ldots$ be IID random variables.
We also consider an independent set of coin flips $Y_1, Y_2,\ldots$.

Let $X_1$, $X_2$, \ldots\ be IID random variables.
We also consider an independent set of coin flips $Y_1$, $Y_2$, \ldots.

\end{document}
• of course, if one is unlucky enough that the second string falls at the end of the line, separating the individual elements will have a better chance of avoiding overfull boxes or badly spaced text ... – barbara beeton May 17 '17 at 0:41
• Usually, thereally is a list ender, telling how many elements there are, like X_N or Y_M. – Scott Seidman May 17 '17 at 0:54

You could just pick another notation for your sets and not worry about dots and commas.

\documentclass{article}
\begin{document}
Let $\{ X_i \}$ be IID random variables.
We also consider an independent set of coin flips $\{ Y_i \}$.
\end{document}