WTH are you talking about here? No one is trying to add to a sum "that equals infinite" as you put it.And I've already pointed out that you cannot add to a sum that equals infinite, regardless if you use it to represent an infinitely small (10^-infinity) or large (10^infinity) decimal. You want to use a rule of thumb to reason out infinitely small numbers when infinite doesn't follow the same rules as other numbers. Your argument is akin to someone insisting that division by zero is possible. Hence the conclusion of your proof has a gaping wound:
RossGR's proof is completely valid. I also posted a version of this proof way back in the thread.
Please show which step of this proof is not valid with a clear and mathematically sound reasoning.