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I am writing a master thesis in maths and I use lots of enumerations in theorems. I am not sure, how I use a comma and period correctly. As I was told, there has to be a comma after an item, except the last, which has to be ended by a period. Like in the following example: enter image description here

But now I have a more difficult enumeration: enter image description here

The items itself contain a period at the end. So I would

  1. not end the first item with a comma

and

  1. not end the second item with a period.

But then I have the impression, that I do not use a certain style continuous.

What do you say?

Lereu
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    Actually, the structure and meaning are clear without any "end" punctuation at all. Seems pretty inconsequential. – Buffy Jan 10 '24 at 15:56
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    Keep in mind that most people here will be used to producing academic texts in English, and their answers will reflect that. I'm not sure you can safely assume the same conventions apply across languages. I suspect you'd be better off asking your supervisor. – Chris H Jan 11 '24 at 14:01
  • For what it's worth, I generally used sentence punctuation in my PhD thesis (submitted in English at a German institution), but did not use punctuation after conditions like those in your second example (for example). I don't remember if I was following any particular style guide or just doing what felt right to me, but there certainly wasn't any criticism of the formatting. – Chris H Jan 11 '24 at 14:13
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    I've read a lot of math, and I'd say that the commas after the 1 and -1 do not usually appear there. As for the others, I might change the first period to a semicolon, but wouldn't worry too much about it. – Mike Jan 11 '24 at 16:29
  • @Mike I would recommend making this an answer – David Raveh Jan 11 '24 at 16:31
  • No mathematician here, but just to suggest another solution I would usually add a colon after "gelten" and would use no other punctuation in/between the equations. – Snijderfrey Jan 11 '24 at 16:54
  • Note that the rules for punctuation are different between English and German. I'm not sure whether that affects the answer in the maths case, but in the question, "not sure, how" and "impression, that" the commas are incorrect in English and should be removed (though I believe they are good in German). – psmears Jan 12 '24 at 12:17
  • Isn't it usual to put the reference to an equation to the right of the equation? Example. – Andrew Morton Jan 12 '24 at 19:55
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    @AndrewMorton in this case, this is acting like an itemized list (like bullet points), so it should be on the left – David Raveh Jan 12 '24 at 20:06

4 Answers4

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I have to disagree with Thomas Schwart's advice (particularly the first sentence—as a matter of opinion, I don't think that properly punctuated mathematics is ambiguous). Mathematical sentences, including sentences which contain notation, should be punctuated in accordance with the normal writing standards of the language being written in.

For further details, I would recommend having a style guide handy. The standard guide for writing mathematics in English is the AMS [American Mathematical Society] Style Guide. The relevant material for punctuation is in Section 12.7. Quoting directly from the introduction to that section:

Mathematical expressions, including displayed equations, are treated as phrases or sentences and are punctuated accordingly (see section 13.4).

There is quite a lot of discussion on lists in Chapter 6, and Section 13.11 is relevant with respect to the punctuation of things in the cases environment.

(Of course, if you are writing for a particular advisor or journal or organization or whatever, and that advisor, journal, organization, or whatever tells you to do something different, then do what they ask you to do.)

Xander Henderson
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The problem with punctuation marks in mathematical formulae is that they can appear to be parts of the notation. I personally would not use them.

The way you decide this for yourself is to look at a copy of a classic mathematical text in your field and then copy their style.

If your thesis supervisor has told you to use a certain style, use that style.

Thomas Schwarz
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    (+1) Your first sentence is something that, over the years, I've felt more and more strongly about, at least in my personal writing when I don't have to conform to styles in place by others (e.g. in my day-job writing and editing work). – Dave L Renfro Jan 10 '24 at 17:53
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    To me, it's really irritating when someone adds punctuation after a URL, and in copying it, the URL doesn't work. A similar paradigm would be part of math. Also, separately, different regions of the world would interpret ',' and '.' differently. – JosephDoggie Jan 10 '24 at 18:11
  • Worse is when a mathematician is so enthusiastic about their result that they add an exclamation mark at the end of the sentence and now you have to guess whether that factorial is part of the formula or not! – Stef Jan 11 '24 at 11:18
  • @Stef while I don't support the use of exclamation marks in this context, one way to do it is to put it in parentheses "we see that x=0 (!)." – David Raveh Jan 11 '24 at 12:57
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    "The problem with punctuation marks in mathematical formulae is that they can appear to be parts of the notation" would you mind providing an example? (And not the exclamation mark/factorial example, as it is pretty rare for an exclamation mark to appear in mathematics.) – David Raveh Jan 11 '24 at 13:07
  • @Stef This seems like a really artificial example, as formal mathematical writing should not have exclamation points in it. Of course, in informal mathematical writing, you can do whatever you want, but then the question is kind of moot, since no one cares what you do on your own time. – Xander Henderson Jan 11 '24 at 14:53
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    Besides the factorial symbol, the question mark symbol is (now) standard for this function. Also, a colon : (sometimes a semicolon ; is used) and a vertical bar | are often used for "such that" in describing a set, and =: is often used for "equality by definition". There is even a double factorial symbol! Although I've never had to deal with a factorial symbol followed by an exclamation symbol, I often deal (my day job) with factorial symbols followed by a question mark. – Dave L Renfro Jan 11 '24 at 14:58
  • @XanderHenderson Let's disagree on this. I have no idea where you draw the line between "formal" and "informal" or why you think mathematicians "should" write the way you like rather than another way. As for your last sentence, I don't know what it is that you call "your own time", but given how much work goes into writing a book, I find the contempt of your comment that "no one cares" extremely distasteful. – Stef Jan 11 '24 at 15:08
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    @Stef It is not contempt nor disdain. What you write on your own time (i.e. for yourself, not for publication or dissemination) is entirely your own business. When you are writing for no one but yourself, you can write however you like. No one else should care what you do with your own notes. With respect to drawing a line between formal and informal, this is how all writing is done---when you are writing in a formal voice, you are following a narrow set of rules (e.g. as set out by a style guide)---that is what it means to write in a formal style. – Xander Henderson Jan 11 '24 at 15:13
  • An informal writing style can be a lot looser, and most people won't care if it follows some particular set of conventions or rules. But you generally aren't going to be publishing informal writing anywhere but, for example, a personal blog. – Xander Henderson Jan 11 '24 at 15:14
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Unless you've been given some guidance from the people writing down rules for theses at your university, just pick a style you like for enumeration from a respectable journal in your field, and use it.

Scott Seidman
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Regarding Satz 3.1.8(a), I would already dispute the assertion that the item itself contains a period at the end. In my view, the first three commas are dictated by the case-structure of the specific mathematical expression*; but the period is in a slot for a global punctuation mark that treats the entire mathematical expression as a black box. So the rule for what punctuation to put there is the same as in Lemma 3.1.6—that is, the period should be replaced by a comma.**

*People have different conventions for punctuation in case-structures, but my main point doesn't depend on whether those internal commas are used (personally I prefer using them as given).

**It is always a valid optinon (at least in English) to replace a comma by a semicolon if the comma is separating phrases that themselves contain enough commas that the semicolon would add clarity.

Greg Martin
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