Punctuation in mathematical writing

[jgens]

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 $i \in \{1,\dots,n\}$, write $\alpha_i = b_{i1}\beta_1+\cdots+b_{in}\beta_n$, where $b_{i1},\dots,b_{in} \in \mathbb{Z}$.

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 $b_{i1},\dots,b_{in} \in \mathbb{Z}$ is technically a noun, I should write something like "... with $b_{i1},\dots,b_{in} \in \mathbb{Z}$" instead.

 

[DeadOriginal]

I think it looks fine but then again I just started learning how to write proofs not too long ago.

 

[Mark44]

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 $i \in \{1,\dots,n\}$, write $\alpha_i = b_{i1}\beta_1+\cdots+b_{in}\beta_n$, where $b_{i1},\dots,b_{in} \in \mathbb{Z}$.

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.

IMO, the commas are helpful.

Edit: I suppose that since $b_{i1},\dots,b_{in} \in \mathbb{Z}$ is technically a noun, I should write something like "... with $b_{i1},\dots,b_{in} \in \mathbb{Z}$" instead.

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 b_is 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."

 

[Fredrik]

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".

 

[CellCoree]

As a scientist, it is important to use proper punctuation in mathematical writing to ensure clarity and accuracy. In this case, the use of commas is not necessary as the sentence is a list of items separated by "+" signs. However, it is also not incorrect to use commas, as they can help to visually separate the items and make the sentence easier to read. Ultimately, the most important thing is to be consistent in your use of punctuation throughout your writing. You can also consult style guides or ask for feedback from colleagues to ensure your writing is clear and easy to understand.