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Q1: If I want to write in a mathematical article, the following sentence:

Consider N real numbers $x_i$...

Q2: Is it better practice to write "$N$" or simply "N"? Similarly, if one is writing:

Let $M$ be a 3-dimensional manifold.

Do I write "$3$-dimensional", or "3-dimensional"?

Q3: when does one use \cdots, and when does one use \ldots? For instance, if I were to write "x_1,...,x_n", is it better to write "$x_1,\ldots,x_n$" or "$x_1,\cdots,x_n$"?

These are 3 questions that always confused me. I would appreciate someone's help. Is there an online document that may tackle similar issues perhaps (including how to break long words)? Could someone please provide a link to that document?

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    Consider $N$ real numbers $x_i$ (N is a math variable), Let $M$ be a 3-dimensional manifold (3 is part of a word and has nothing to do with math), x_1, \dots, x_n (with mathtools loaded \dots is intelligent; in any case in that place you should go with \ldots, but as I say, \dots is enough).
    – Manuel
    Dec 27, 2017 at 15:40
  • Thank you so much. I did not know about \dots in particular! Thank you. I am also reading a document by the AMS on best practices, which is also very helpful.
    – Malkoun
    Dec 27, 2017 at 15:42
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    And don't forget the non-breaking space: Consider $N$~real numbers…, in case these words are typeset at the end of a line. (Not in this peculiar case of course, but who knows, after a copy-paste…) Dec 27, 2017 at 16:05
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    @Manuel I would definitely write $3$-dimensional if it is to be a numeral, cf. $n$-dimensional, but one might also write three-dimensional Dec 27, 2017 at 16:14
  • Thank you @FranckPastor. This is helpful too, though I deal with it the lazy way, by not writing $~$ here, and dealing with "bad" cases, as they occur. I also have issues with some words at the end of lines going over the margins, and not being properly hyphenated by LaTeX. But this is another question, and so I guess should be in another post (though I am sure I will find an existing post dealing with this issue!).
    – Malkoun
    Dec 27, 2017 at 16:14

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