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In the following sentence

If all $f(x_j), j=1,\dots,N$ are positive, then ...

Do you think there should be a comma after the $N$? I always considered the math as a single unit and read the sentence as

If all [MATH] are positive, then ...

Accordingly I only put commas when the surrounding sentence required them, as in

Given $f(x_j), j=1,\dots,N$, our goal is to ...

I am asking because I observed a lot of authors not following my thinking. However, there are also some that more or less do put the commas as I do, so I wondered if you know about guidelines regarding this question or simply have a definite opinion about it.

Bananach
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    Personally, I like to treat my math as if it's part of the sentence. Also I don't like to have two different math statements next to each other without words. I'd do something like "Given $f(x_j)$, where $j=1,\ldots,N$, our goal is to..." –  Feb 11 '16 at 08:14
  • What about the first example? "If all $f(x_j)$, where $j=1,\dots,N$, are positive" breaks the sentence apart. "If all $f(x_j)$ are positive, where $j=1,\dots,N$" breaks the math apart. – Bananach Feb 11 '16 at 08:24
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    I don't see what's wrong with "If all $f(x_j)$, where $j=1,\ldots,N$, are positive", but you can also do "If $f(x_j)$ is positive for all $j=1,\ldots,N$" –  Feb 11 '16 at 08:30
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    The two phrases are grammatically different. In the first, there shouldn't be a comma after $N$; in the second, there should be one after "positive". Forget about whether there's math present: this would be true if the sentences were "If each of John, Mary, and Joe are happy, then ...", and "Given that we have amassed all the data, our goal should now be to...". – BrianO Feb 11 '16 at 08:32
  • @BrianO That they are gramatically different is exactly the reason of my usage so far. However, an argument for a comma after $N$ in the first sentence is: $j=1,\dots,N$ is a restrictive clause initiated by a comma and should thus be terminated by a comma. I don't know the grammatical terms, but an equivalent without math would be: "If the kids, and by kid I mean everyone under the age of 18, are happy, then ..." – Bananach Feb 11 '16 at 08:38
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    But "If all $f(x_j), j=1, ... N$" isn't a restrictive clause, it isn't even a clause. You don't have a full clause until you get to the end of "are positive", where of course a comma is required. It reads badly and goes "bump* to have a comma after $N$. You wouldn't write "If Moe, Larry, and Curly, are funny, then ...", and you wouldn't write "If the integers, are rationals, then...". – BrianO Feb 11 '16 at 08:41
  • What I am saying is that the $ j=1,\dots, N $ can be regarded as a restrictive clause – Bananach Feb 11 '16 at 08:52
  • @BrianO I believe the OP is saying that you can read the sentence as "Given $f(x_j)$, where $j=1, ... N$, - our goal is to...". In this case the comma is clearly recommended. – Jack M Feb 11 '16 at 08:58
  • @JackM, I agree that in the example you just gave, in the presence of "where" a comma is called for. But that's the 3rd highlighted fragment, not the first. – BrianO Feb 11 '16 at 09:02
  • @BrianO The first fragment can be read that way as well, imagine there's an implicit "where" or "with" after $f(x_j)$. – Jack M Feb 11 '16 at 09:03
  • @JackM I can imagine all sorts of things being there which in fact aren't. As it stands, it's at best awkward, worse, and arguably wrong to put a comma there. However, I don't want to flame about this. – BrianO Feb 11 '16 at 09:08
  • @BrianO I found "Mathematics into Type" by the AMS (available online), which says in Section 2.6.3 that the comma always belongs there. – Bananach Feb 11 '16 at 09:26
  • @Bananach Do you have a link? I only found a version behind a paywall. – BrianO Feb 11 '16 at 09:31
  • Does ftp://ftp.ams.org/ams/author-info/documentation/howto/mit-2.pdf work? – Bananach Feb 11 '16 at 09:41

1 Answers1

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To summarise those comments with which I agree: the following are preferable.

If all $f(x_j)$ are positive (as $j$ ranges from $1$ to $N$), then…

If for all $j$ with $1 \leq j \leq N$ we have $f(x_j)$ positive, then…

A little more clumsy:

If all $f(x_j)$ (where $j = 1, \dots, n$) are positive, then…

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Patrick Stevens
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