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I don't know whether there is any rule about this. But I've been wondering that if a math question is ended with an exclamation mark, would it be misinterpreted with "factorial"? For example, consider this question below.

Calculate $6! \times 2!$

Does it mean that we should calculate $6! \times 2!$ or $6! \times 2$?
But now if we write the question as below:

Calculate $6! \times 2!!$

Does it mean that we should calculate $6! \times (2!)!$ or what?
Now if we write this instead:

Calculate $6! \times 2!.$

it's clearer that we must calculate $6! \times 2!$. But grammatically speaking, should an exclamation ended with an exclamation mark?

I know it's a kind of weird question, but what do you think?

RANGGAJAYA CIPTAWAN
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    If anything, you should probably ask it here: https://math.meta.stackexchange.com/ – morrowmh Dec 21 '21 at 04:38
  • Ahh okay thanks for the advice – RANGGAJAYA CIPTAWAN Dec 21 '21 at 04:40
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    Why do you think "$6! \times 2!!$" is unambiguous? ("There are more notations in math and logic, Horatio, than are dreamt of ...") – Eric Towers Dec 21 '21 at 04:40
  • Oh yeah that's right. For example 4!! can be interpreted as (4!)!. Thanks for the insight. – RANGGAJAYA CIPTAWAN Dec 21 '21 at 04:43
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    In mathematical text, I’d suggest that exclamation marks should be reserved for denoting factorials. If you want to express surprise or emphasis, find some other way to do this in cases where it could cause confusion. – bubba Dec 21 '21 at 04:48
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    In a math textbook or paper, it is on the writer to be clear and unambiguous. And so generally speaking, an exclamation mark should almost only be used in mathematical expressions, to avoid overloading that notation. If the writer really, really wanted to express exclamation, he could say e.g., "calculate $6!×3!$, please!". [And even that is a bit silly, "calculate $6!×3!$" i.e., $6!×6$ is simply better.] – Mike Dec 21 '21 at 04:50
  • Does this answer your question? Sentence ending with a number and an exclamation point – 311411 Dec 21 '21 at 04:57
  • For handwriting at least, I came up with a convention that an outlined exclamation mark is non-mathematical, i.e. for emphasis as in "Wow!" Something like this "a": https://tex.stackexchange.com/questions/125578 – 311411 Dec 21 '21 at 05:00
  • If it is clear from the topic that factorials do not occur, the exclamation mark is not a major problem, and it is anyway only a problem if it occurs behind a number or a variable or a factorial expression. Nevertheless, it is usually not needed and therefore best is to simply avoid it. – Peter Dec 21 '21 at 13:57
  • There is a joke (I cannot however remember it) where the point is that the exclamation mark must be interpreted as a factorial to make the statement correct, – Peter Dec 21 '21 at 13:58
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    By the way, in the case of "$2$" , the exclamation mark does in fact not matter. – Peter Dec 21 '21 at 14:02
  • (1) The AMS style guide seems to be silent on this issue, hence it is between you and your editor / instructor / advisor / reviewers / whoever. (2) I would suggest that "$2!\cdot 6!.$" is unambiguous, and that $2!\cdot 6!!$ often denotes the double factorial. I would avoid using $!!$ unless you mean the double factorial. (3) Formal mathematical writing should probably avoid exclamation points, anyway. – Xander Henderson Dec 21 '21 at 14:03

2 Answers2

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There are no "official" rules for how you combine symbolic math expressions with the surrounding natural language, but you should obviously avoid ambiguity. Putting an exclamation mark right after a numeric expression where it could be interpreted as a factorial is likely to be confusing.

Also, conventional math writing (at least what I'm familiar with) is pretty dry and unemotional, so readers are more likely to interpret an ambiguous $!$ as a factorial than as an exclamation.

Karl
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While writing on a blackboard, for an exclamation point "in English" I use a "bubble font", and/or often parentheses, as in chess notation: (!?) and (!) and (?) and so on...

paul garrett
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    I once wrote something like "Evaluate $f$ at $x=7$!" on a blackboard. One student asked if I meant the factorial, and for once I had a quick idea and changed what I wrote to "Evaluate $f$ at $x=7$, please!" Lesson learned: Politeness can help making things less ambiguous too! – Torsten Schoeneberg Dec 21 '21 at 22:22