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For example, if I want to say something like

Let x_1, ..., x_n be real numbers.

should I use

Let $x_1, \dotsc, x_n$ be real numbers.

or

Let $x_1$, $\dots$, $x_n$ be real numbers.

Note that if one lists only two objects a, b, then

Let $a$, $b$ be real numbers.

should be used instead of something like

Let $a, b$ be real numbers.

since the comma is part of the text (and not of the mathematical notation), see "$a, b$" vs. "$a$, $b$" or $a,\ b$, and $c$ vs. $a$, $b$, and $c$.

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    Use \dots; \dotsc is necessary in cases such as a_1,a_2,\dotsc where the nature of the dots cannot be determined by examining the next token. – egreg Aug 13 '18 at 16:35
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    Related/duplicate: tex.stackexchange.com/questions/122491/4427 – egreg Aug 13 '18 at 16:36
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    Let $x_1$, $\dots$, $x_n$ be real numbers. seems needlessly complicated, but I can see where you are coming from... – moewe Aug 13 '18 at 16:47
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This is partly a math question and partly a tex question.

The expression represents a continuum, so the spaces around the dots should be uniform between the commas. This will be accomplished only by including the entire expression in a single math environment.

Now for the tex part. This is best expressed as $x_1, \dots, x_n$. \dotsc isn't needed because it's possible to determine the position -- which should be on the line -- from the enclosing commas (as mentioned in a comment by @egreg).

Finally, althougn this won't break by itself if it happens to fall at the end of a line and will overflow into the margin, that can be remedied by inserting \allowbreak after whichever of the commas will result in the most satisfactory realignment of the paragraph.

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    @dexteritas Please read the note at the end of barbara's profile. The "wrong" spelling was intended. – campa Oct 24 '19 at 15:49
  • @campa Okay, I didn't know that. Nevertheless, I think that a correct spelling is appropriate on this page. Otherwise every user could think of his own semantic meaning for correct and wrong spelling, then it becomes confusing ;) Instead, if necessary, I would include the hint that it is only one's own opinion in the text. – dexteritas Oct 24 '19 at 16:06
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In my opinion, you should write "Let $x_1$, \dots, $x_n$ be real numbers." Two or many, in a text context they should be treated accordingly.

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    while breaking up the math string is quite acceptable if there are only two non-dots elements, the presence of the dots makes this a bad idea. breaking up the math is okay in a string such as if $a$, $b$, or $c$, where uniformity of spacing isn't a consideration. – barbara beeton Oct 1 '18 at 12:58

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