I met the following problem in a math paper writing:

Suppose that a_i, i=1,2... are elements which satisfy some common property X. Then should I say

"a_i has property X" or "a_i have property X"?

I want to say all the elements have this property, but I just don't want to write "a_i, i=1,2..." at each time.


As a mathematician, I would tell you the first is correct, but in the latter case it would be more common to see

The a_i have property X.

By which we are shorthanding 'The set of a_i have property X.'

Whether or not you want to refer to all of them, or just one, is a matter of how you will be referring to them going forward. If you intend to work with a single a_i from here out, talk about a single a_i in this sentence. If you intend to continue working with the whole set, use the plural here as well.


a_i has property X

Would be correct as a_i is a singular set, of which , i=1,2 are the individual elements.

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