When writing down an infinite sum (or product, union, intersection), in order to achieve maximal generality, one has to use an index set, i.e. not write "i = 1 ... infinity", but instead "i element of I". This allows for the operation to be performed on an uncountable number of operands, not just a countable one. For reasons explained in finite vs. countable vs. uncountable, this can be a crucial difference.