The title says it all (I'm referring to the case, when writing for example an article to be published or something similar - something where the writing itself should also be of quality).
Example: "Let $A_1,A_2,\ldots,A_n$ be subsets of a set $L$ and $f:L\rightarrow L$. Then define $B=\cup_{i=0}^n A_i$ and $C=\cup_{i=1}^{\infty} f^i (A_2)$, where $f^i$ is $f$ iterated with itself $i$ times."
So (in this example), would it be a problem to use $i$ twice as an index variable the ranges over different sets ? Or is it ok to think of $i$ as being define like a (lets do a computer-science analogy) "local variable", that is only used to create the object "in" which it is defined ($B$ for example) and after the object is created, the variable is "freed" again (so it can be used again to define $C$) ?
If it is NOT okay to do that, when is it allowed to use the same symbol again, after its first use ? After half a page ? After two pages ? In index-heavy proofs one would very soon have finished all letters commonly used as indices, of one would always have to use a different letter. And indexing sets with letters like $x$ or $f$ seems even worse style to me (ok, maybe there are areas in math, in which this would be common practice, but I don't know any).