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I am pondering about comma rules/conventions in mathematical writing. Consider the following example:

We prove that the variables

$A, \; B, \; C$

are equal. Hence the equations

$A = B, \; B = C, \; A = C$

are valid.

When typing a document, the mathematical text roughly looks like that when the mathematics is put into display style. The above is equivalent to

We prove that the variables $A$, $B$, and $C$ are equal. Hence the equations $A = B$, $B = C$, and $A = C$ are valid.

It seems to be customary that in the transition from "mathematics in normal text" to "mathematics in text with displayed mathematics" enumerations are put down without using "and" before the last item. The reason is that normal text in displayed equations looks awkward.

Question: do you retain the commas in the enumerations when there is a line break? I presume you would always do because the line break is just formatting, and without commas you obviously have ambiguities.

Question: when do you put commas after the displayed enumeration? My guess is that the usage of commas in the "original" text is authorative.

I have seen all options in writing, including mixed style throughout the document.

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Interesting that you pointed out the following that I think most who write mathematics would agree with, and might do naturally.

Enumerations [in the display-math environment do not include] "and" before the last item.

You give a reason that "normal text in displayed equations looks awkward", although if you use \text{ your text } this shouldn't be a problem. The true reason might be that including the 'and' is cluttering, therefore not necessary.


Now, to actually answer your questions...

If I'm interpreting your first question properly,

Do you retain the commas in ... enumerations when there is a line break?

I think you're talking about the display-math environment (hence the reference to a 'line-break'). My answer, then, is YES. The reasoning you guessed for yourself:

without commas you obviously have ambiguities.

As for your second question,

When do you put commas after [an] enumeration [written in the display-math environment]? My guess is that the usage of commas in the "original" [(non-display-math)] text is authorative.

Since you haven't provided a specific example here, I will answer with a general rule that will help you, taking a page from Richard Hammack: "Clarity is the gold standard of mathematical writing. If you believe breaking a rule makes your writing clearer, then break the rule" (Hammack, p. 109, Book of Proof, Edition 2.2).

Also, in case you were wondering and more towards your question, sometimes punctuation in the display-math environment is entirely avoided, as long as the writing is clear.

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