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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Example sentence:
The $x_i$s form a sequence.
The $x_i$'s form a sequence.
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."
Neither. The $x_i$ form a sequence.
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: