>>13795420IF you had just taked x to be a positive real number, then the answer would be extended real number +infinity. The same applies for any sum of an uncountable number of positive elements. This is actually an important fact in measure theory, although I forget exactly why. I think it has something to do with countable additivity or something.
However, you asked about the sum over all real numbers. This would have to be either zero or undefined. My guess the latter, but I bet if you asked a logician, they might be able to find some non-standard model, where the sum is 0.
