Which one is correct, $x_i$s or $x_i$'s?
Example sentence:
The $x_i$s form a sequence.
The $x_i$'s form a sequence.
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6$\begingroup$ Both are terrible. $\endgroup$– Brendan McKayCommented Jan 5, 2015 at 8:16
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10$\begingroup$ If you want to use such a format, include the apostrophe. The other way looks weird. Other situations outside of math: "his grades are all A's" (versus "his grades are all As"), "dots your i's" (versus "dot your is"), or "mind your p's and q's" (versus "mind your ps and qs"). From the viewpoint of clarity I think apostrophes belong there. This use of the apostrophe after single letters or numbers to indicate plural is not the standard grammatical function of an apostrophe, but c'est la vie. $\endgroup$– KConradCommented Jan 5, 2015 at 9:35
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5$\begingroup$ @YemonChoi: for PDE’s vs. PDEs, it’s certainly a general English usage question — and indeed it’s already asked and well-answered on english.stackexchange. But for $x_i$ vs. $x_i$s vs. $x_i$’s, the usage and conventions are pretty specific to mathematical writing, so it seems reasonably on-topic here to me. $\endgroup$– Peter LeFanu LumsdaineCommented Jan 5, 2015 at 11:51
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3$\begingroup$ @PeterLeFanuLumsdaine My experience editing mathematical writing, having my writing edited, disagreeing with the copy-editors of AMS and OUP on whether "Helson set" and "Hochschild cohomology" require the definite article, and reading Fowler, make me fear this is a topic where discussion here will just devolve into anecdotes and selective quoting of conflicting grammar guides $\endgroup$– Yemon ChoiCommented Jan 5, 2015 at 11:54
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3$\begingroup$ To all you native English speakers that might shake their head in disagreement with both choices, just remember that the official language of science is Broken English. :-) $\endgroup$– Asaf Karagila ♦Commented Jan 5, 2015 at 12:13
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3 Answers
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I prefer adding a noun. You can decline the noun and remind the reader of the type of the object in question. For example: "The numbers/points $x_i$ form a sequence." "One of the numbers $x_i$ has to be an integer."
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Neither. The $x_i$ form a sequence.
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6$\begingroup$ In speaking, many mathematicians would pluralise it. Why not in writing also? Both options suggested are visually awkward, true; but it’s also awkward, in a different way, when orthography fails to follow speech. $\endgroup$ Commented Jan 5, 2015 at 9:26
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3$\begingroup$ @PeterLeFanuLumsdaine Oh, you want a phonemic orthography?. That battle is already lost when you chose English. $\endgroup$ Commented Jan 5, 2015 at 10:41
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1$\begingroup$ @YuichiroFujiwara: sure, yes. I’m not advocating spelling reforms. But when there are multiple existing conventions (as in this case), closeness to speech can reasonably be a factor in the choice between them. $\endgroup$ Commented Jan 5, 2015 at 10:49
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1$\begingroup$ @YuichiroFujiwara (continuing the possibly unnecessary seriousness): A less prescriptivist approach is exactly what I’m trying to advocate! I believe that in speech, the explicitly-pluralised-with-a-[z]-phoneme version is more common/natural than the zero-pluralised version (it’s at least a common choice), and so saying “you can’t write that, because it looks terrible” (or “…is wrong”) is an unreasonably prescriptive stance. Unless you read the zero-pluralised written form as representing the explicitly-pluralised spoken form — but I don’t think most people read it that way. $\endgroup$ Commented Jan 5, 2015 at 11:21
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3$\begingroup$ @PeterLeFanuLumsdaine I understand what you mean. I just meant closeness to phonetic realization doesn't justify particular written form, and that "justify" doesn't make sense unless we're trying to set up a publisher's style guide or something. I'm sure you understand why, and I don't think many users on MO get the point. (See how people are arguing which is correct and which is wrong...) If we want to be serious, OP's question is already not good; a better (but off-topic) question would be which is more common, which is your choice and why, which is preferred by this journal's style, etc. $\endgroup$ Commented Jan 5, 2015 at 11:45
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Shall you use one of these, according to Oxford Dictionaries Online, you should only use an apostrophe "for the sake of clarity", therefore opting for the first option ($x_i$s).
There are cases, like this in Statistics, where you can use the plural, for example, for a variable as the p value. You would then write ps to show the use of multiple p values.
However, these are different variables, with possibly unrelated calculations (even though the formula is the same). In the case of a sequence, $x_i$ is already a generic term, representing each element or the sequence itself. You can then write:
- "the sequence $x_i$", or
- "the sequence $(x_i)$"