Let x1, . . . , xn be a collection of mathematical objects.

When I refer to them, do I have to say the xi’s or just the xi?

Edit: In this article (written by an American mathematician), one can read

... is the set of all x's which have the form ...

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    I think it may depend on context. In some circumstances "all x" may be appropriate. – Andrew Leach Sep 3 '13 at 6:10
  • I don't think I've ever seen this come up in a textbook or paper. There's always going to be a better, less awkward way to phrase it, although it'll depend on context. – starwed Sep 3 '13 at 6:24
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    I think the real problem here is your use of the definite article the. Usually one would say that xᵢ is always positive, or perhaps that all xᵢ are positive. – tchrist Sep 3 '13 at 10:41
  • Mathematicians seem to avoid the plural, with construct like for all _i_, x_i is non-negative. – MSalters Sep 4 '13 at 13:20

Interesting question. The notation "x_i" refers to all the x's, so it should be taken as plural. I think if you find a math book, you'll find things like "... the x_i are all positive".

| improve this answer | |
  • I don’t think that you can use the there. – tchrist Sep 3 '13 at 10:41

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