Some tricky demonstration that seems to be some freak non-sense, similar to the 1+1=3 buuuuut that astonishingly it is used in string theory!
The week point from my amateur opinion is precisely the 1-1+1-1+1-1… = 1/2. As far as I have been tought in my dear Engineering School that sum does not converge, therefore limit does not exist. Or as our super-smart MatLab would say: NaN (not a number).
I get that mathematically you can get super rigorous demonstrations on that, which Engineers and Physics may believe but not understand. So, once we have reach this point of taking sides, what makes me flip is that actually that final solution can be the answer to many problems in string theory. It’s a way to say that we are missing soooo much about the deep explanation of things.