Plural for math notations

I have a question about the usage of plural in mathematics in the following context.

Suppose we have functions f₁, f₂, ⋯.

Which of these sentences is correct (if any)?

1. Among the functions f_i's there is no repetition.
2. Among the functions f_i there is no repetition.
3. Among the functions f_i's there are no repetitions.
4. Among the functions f_i there are no repetitions.

The focus is on whether I should use 's or not. Also, is or are.

You can think of "f_i" as shorthand for the list of individual functions "f₁, f₂, ..., f_n, ..." Understood as such, the correct sentence would be:

Among the functions f_i there are no repetitions.

This would be a shorthand for:

Among the functions f₁, f₂, ..., f_n, ... there are no repetitions.

Notice the plural "functions" and the use of the plural verb "are".

Alternatively (and maybe less standardly), you could think of "f_i" as a kind of count noun which applies to every function in the list. Understood as such, the correct sentence would be:

Among the f_i's there are no repetitions.

Normally, you would not use an apostrophe in a pluralization. But you can get away with using the apostrophe here (even though it is not indicating possession), just like you can get away with using it to make a pluralization for something like a letter, as in:

There are two a's in the word actual.

The apostrophe is needed to forestall confusion.

I don't think there is hard and fast rule about which is the right way to view the mathematical convention of using "f_i". Your best bet is to pick one way of understanding it and stick to it. Or else forget about it entirely and just say:

Among the functions there are no repetitions.

After all, why muddy the page with needless formalism?