# Fun with factorials

We had fun with this on Twitter a while ago. I’m just posting on the blog for the more permanent record.

If I end a sentence with a factorial, do I need a period?

That is, which of the following should it be?

(1) The number of ways to arrange 4 cats in a parade is 4!.

or

(2) The number of ways to arrange 4 cats in a parade is 4!

UPDATE: After being taken to task for a missing question mark by one Chris Lusto, I have corrected the error. I regret the oversight in a post about punctuation!

### 5 responses to “Fun with factorials”

1. Karim

Probably the former. The factorial (!) isn’t punctuation. (Neither, for that matter, is a parenthesis which I imagine should be written as 2(x+5).)

Of course, excitement about factorials might lead to confusion. The number of ways to arrange four cats is 4!! That’s 24!! No, wait….6.2E23!!…

• To make matters even worse, should you interpret 4!! as (4!)! = 6.2E23, or as a proper double-factorial, in which case 4!! = 8? Anyway, I vote yes to punctuation. I think of the expression as being embedded in the sentence, and so the sentence must be still be well formed if you replace the expression with something else that doesn’t superficially seem to have punctuation at the end because we have a finite number of typographical symbols to use for stuff.

2. Well, without a period at the end of your sentence I’m feeling like you’re yelling the wrong answer at me!
And yes, I am kind of yelling at you!

3. By the way, you posed a question at the very end of the post with no question mark in sight. In fact, there’s no punctuation at all to conclude your last sentence. Do you need a question mark at the end of a question that has a list of complete sentences in the middle of it?. Especially if the last of those sentences ends with a factorial?(!) This section seems to be missing from my copy of Elements of Style.

4. Ending a sentence with a factorial is something up with which I will not put. Why not just say there are 4! ways to arrange 4 cats in a cat parade?