Notation for elements of a vector in English language

Question

I am writing a non-math text in English. In some parts of the text I have to mention the elements of a vector. Suppose that the vector is $\boldsymbol Y=(y_1,y_2,\dots,y_n)^T$, and I refer to any its elements as $y_i$.

Which of these expressions is more appropriate?

1. The $y_i$s are ...
2. The $y_i$'s are ...
3. $y_i$s are ...
4. $y_i$'s are ...

I originally used 1. but the editorial team replaced it with 4.

I asked a native speaker and he told me that the " ' " should not be used because it indicates belonging. But it could be that using 4. corresponds to a tradition of the field.

Thanks in advance.

Answer 1

If this is the start of a sentence, I cannot understand why they removed "The". Maybe if we see the full sentence it would make sense, but I'd be surprised.

And as for the apostrophe, I tend to use them, mostly because a string of mathematical symbols isn't a word, and isn't read like a word, but the pluralizing "-s" is a regular weird element, so I like there to be something to separate them. But I'm not consistent, can't rigorously justify it, and would accede to a style guide that says not to use them. (Check out "grocer's apostrophe" to see some of the strange things native English speakers do with apostrophes.)

So I would write #2, accept #1, and push back a little on #3 or #4.