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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, 2013 at 6:10
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    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, 2013 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, 2013 at 10:41
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    Mathematicians seem to avoid the plural, with construct like for all _i_, x_i is non-negative.
    – MSalters
    Sep 4, 2013 at 13:20
  • You assign a symbol to the set. X = {x1, x2, ..., xn}. You may need to define additional symbols, for instance, you may need to define a symbol for odd indices.
    – Phil Sweet
    Nov 16, 2021 at 2:23

2 Answers 2

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Interesting question. The notation xᵢ 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 xᵢ are all positive".

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  • I don’t think that you can use the there.
    – tchrist
    Sep 3, 2013 at 10:41
  • Such that x subscript i is positive.
    – G. Rem
    Nov 15, 2021 at 21:28
  • @G. Rem: You can cut-&-paste, and I'll delete: Such that xᵢ is positive. Nov 16, 2021 at 13:58
  • @Edwin Ashworth The answer to the universe isn't a loaded question. As such, it's too short to post up here. But, I will say that it's about relating all the physical quantities in five simple steps while, at the same time, working the mathematical theory of everything in which all numerals thus instantly align. I know this because, yesterday, after forty years of staring at the same puzzle, I found the five steps.
    – G. Rem
    Nov 16, 2021 at 16:34
  • @G. Rem Replacing 'x subscript i is positive' with 'xᵢ is positive' seems simpler. Nov 16, 2021 at 16:53
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When I refer to them, do I have to say the xi’s or just the xi?

No xi...xn is the set of x

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

might be clearer as

... is the set of x in which x has the form ...

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