Specifying sets where/with/for

Question

My main interest is in the mathematical context, where one denotes a set of objects with indices. I can imagine 3 cases :

Let xₙ for n=1,2,... denote all objects ...
Let xₙ with n=1,2,... denote all objects ...
Let xₙ where n=1,2,... denote all objects ...

I would tend to use 2 but I was told this sounds strange.

LPH · Answer

I would say that "with" is not a likely choice, but in fact it is possibly used more often than "where", and "for" is chosen most often: ngram.
In this ngram are included all cases in which n is fixed and equal to 1, but I think it doesn't matter.

Specifying sets where/with/for

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