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Punctuation in mathematical writing

  1. May 25, 2012 #1


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    Recently I went through a bunch of my old solution sets and realized that I've been quite sloppy with my use of punctuation; in particular, examining the quality of my writing in solution sets over a period time, it appears that the lack of proper punctuation is getting more and more pronounced. So, in an effort to fix this trend, I have been trying to use proper punctuation in all of my writing. However, today I came across a sentence that I am uncertain how to punctuate properly, and I was hoping that some of the member of PF could help me out on this one. Here is the sentence:

    For each [itex]i \in \{1,\dots,n\}[/itex], write [itex]\alpha_i = b_{i1}\beta_1+\cdots+b_{in}\beta_n[/itex], where [itex]b_{i1},\dots,b_{in} \in \mathbb{Z}[/itex].

    My question is whether or not the commas used above are correct and/or necessary. Off the top of my head, I can't think of any rules that necessitate the use of the commas, but when I write the sentence above, I am naturally inclined to use the commas.

    Edit: I suppose that since [itex]b_{i1},\dots,b_{in} \in \mathbb{Z}[/itex] is technically a noun, I should write something like "... with [itex]b_{i1},\dots,b_{in} \in \mathbb{Z}[/itex]" instead. :grumpy:
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  3. May 25, 2012 #2
    I think it looks fine but then again I just started learning how to write proofs not too long ago.
  4. May 25, 2012 #3


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    IMO, the commas are helpful.
    No, "##b_{i1},\dots,b_{in} \in \mathbb{Z} ## " is a mathematical statement, which makes it more akin to a declarative sentence than to a noun. The bis make up the subject, and "##\in Z##" is the predicate. You can use either "where" or "with," and I doubt that anyone would notice, although I lean a bit toward "where."
  5. May 25, 2012 #4


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    It's not so much about grammar as it is about where the reader should make short pauses. In this case, it's natural to make a short pause at both places where you put commas, so I think it would look weird to omit them. "Where" sounds better than "with" to me. "With" sounds better in this rewrite:

    For each ##i\in\{1,\dots,n\}##, let ##\alpha_i## be a linear combination ##b_{i1}\beta_1+\cdots+b_{in}\beta_n## with ##b_{i1},\dots,b_{in} \in \mathbb{Z}##.

    I assume that's what you meant. Here I prefer to not use a comma before the "with".
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