> A sum of an infinite set is defined as a certain limit. Through convention alone. We have asserted this definition.
> You have contradicted yourself. A sum of an infinite set is a limit. > How else would you define a sum of an infinite set?
Well I think it is clear that the geometic series that represents 0.999... would sum to 0.999... yet the limit is 1. Defining the sum of an infinite set is a convenience of notation so that we need not append lim n-> infinity to the beginning of every infinite series. In my own studies I append just such a thing.
> You need to think again about what an infinite sum means. >
Perhaps you may find it beneficial to ponder the relation an entity has to its limit.