Let's take our sum to infinity where the sum is supposed to be -1/12. Then let's add -1/12 to each side, and the sum is now zero. Am I missing something? Actually the whole edifice of this folly seems to be that these people treat infinity as if it were a number. Now if I can add 1/12 to infinity, it really wasn't infinity anyway. The series cannot converge unless there is a fudge factor, and that fudge factor is a game on paper, (and in some peoples' heads), that doesn't exist in nature (and logic). After all, nature doesn't work with infinitesimals: The shortest time is Planck time is 10**-43 seconds, and the shortest distance is 10**-35 metres. These are not because our tools are not good enough to measure them, it's because these are the smallest packets of time and distance that occur in nature. So the modern day versions of Zeno's paradoxes fail because they arbitrarily assign values to infinity and infinitesimals when required, and remove them when it doesn't suit the purpose. Infinity is still a theoretical, and non-real concept. If nature doesn't use it, then neither should we.