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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?

closed as primarily opinion-based by Werner, Stefan Pinnow, user31729, Troy, marmot Dec 29 '17 at 4:41

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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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 '17 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 '17 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…) – Franck Pastor Dec 27 '17 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 – Andrew Swann Dec 27 '17 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 '17 at 16:14