# What do you do when a sentence ends with a factorial?

Consider the following sentences which utilizes the mathematical factorial operation:

or

The equation is given by

f(x) = (x+4)!.

Typically in mathematical writing, an expression in a sentence is treated as a word and is therefore punctuated accordingly. But in this case, a period following an exclamation point looks awkward. Would a period still be used here to indicate the end of the sentence?

• What do the other articles in the journal do? Commented Feb 6, 2019 at 2:16
• Yes. ---------- Commented Feb 6, 2019 at 4:53
• Enclose the whole item in parentheses of some sort, e.g. The answer is {5!}. or The equation is given by {f(x) = (x+4)!}. [Or if that particular kind of symbol has a special meaning, choose another - even quotation marks will do.] Note also that some style guides say not to put punctuation at the end of an indented quote, so maybe your second example doesn't need a period at all! :-) Commented Feb 6, 2019 at 6:48
• Look up the relevant style manual and let us know. Good Luck.
– Kris
Commented Feb 6, 2019 at 7:25
• I can't find any examples of this case. Commented Feb 6, 2019 at 19:14

The manual of style of the AMS advises:

Each mathematics equation reads as a clause or sentence and is punctuated accordingly. Authors, however, sometimes leave displayed math unpunctuated. Insert commas and periods as needed so that the equation(s), the preceding text, and the following text together read grammatically. Follow CMS, sections 12.18–12.20, for punctuating mathematical expressions and elided lists, operators, and relations.

This implies that you can choose.

I never punctuate displayed math. The capitalization, or lack of it, of the next line, the vertical spacing, and the indentation are punctuation enough. I would use a period after an inline equation, specially after a factorial, otherwise it is ambiguous if the sentence is an exclamation or an equation involving factorial.

If every sentence is required to end with a punctuation mark (which is reasonable), then IMO it's better to punctuate to avoid ambiguity.

With this convention, the sentence

is exclamatory.

Note that the above convention is especially important when posing a question involving a factorial expression: