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Here is an example:

Theorem 1 (Important Theorem). Consider f(x). If something, then

 1. The function has property A:

                  f(x) = g(x).

 2. The function has property B:

                  f(x) = h(x).

My question is the following:

  1. do I capitalize the first letter of the bullet points?
  2. do I include punctuation after the equation?

I typically aim to ensure mathematical expression follow the rules of grammar, but I am stuck here. If I don't capitalize the first letters, then I am not sure how to punctuate the equations.

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3 Answers 3

4

I agree with you that mathematical formulas are usually sentences or parts of sentences and should be punctuated accordingly. This makes your example rather difficult if you don't want to change the words. I'd capitalize neither of the two bullet items, I'd put a comma after the first equation, and I'd put a period after the second equation. That doesn't look very good, and besides it would really need "and" between the two bullet items. So I suggest trying an alternative wording. Here's the first that occurs to me.

Assuming that the equations are intended to define (or summarize) properties A and B, a better solution would be to change the introductory "If something, then" to "If something, then the function has the following properties." Then, instead of numbering the bullet items as 1 and 2, label them as A and B. (Even if A and B are words or phrases, you can use them as labels in LaTeX's "description" environment.) And put periods after both equations, since they're now stand-alone sentences rather than clauses in the "If something ..." sentence.

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This is a matter of taste. I would:

  • Put a colon after "then".
  • Capitalize the first letter of the bullet points.
  • Put a period at the end of each bullet point, just like in this list.

The main principle at play here is that you may break any of the rules of formal writing for the purpose of clarity. The subordinate clauses in the bulleted list are themselves complete sentences, so when you're reading them you expect capitalization and punctuation. It doesn't matter that they're formally also part of one long sentence; as the reader, you've forgotten that by the time you're there.

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I'm no academic or mathematician but punctuation in the equation seems like it could only go wrong. Besides, I never do it when writing stuff and have never seen it done. It never even occurred to me someone would try doing that until I saw this question.

Put another way, what's the point of giving the equation its own dedicated line for clarity if you're just going to throw punctuation into it?

Yes, capitalize. There's no rule that says you must or must not capitalize bulleted items, but this isn't just a bulleted item; It's a phrase or sentence and will look very strange without capitalization.

https://www.grammarbook.com/punctuation/colons.asp

If you're hung up on the rules, generally, the answer is to do what looks good to your eye.

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