Comments by "EebstertheGreat" (@EebstertheGreat) on "0.577 (extra footage) - Numberphile" video.

@austinbryan6759 The series diverges. It diverges "to infinity" if you like, and it can be assigned the value +∞. But there are stronger summability methods that can assign finite values to divergent series. The zeta-regularized sum is -1/12, because ʒ(-1) = 1/12. Both these things can be true at the same time. We don't need some philosophy behind what the "true sum" is. There is no classical sum, because the series diverges. There is a zeta-regularized sum. That's just how it is.
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@TheProudHeretics The series is divergent. So there is no sum in R, or if you prefer, the sum in R̅ is +∞. But the zeta-regularized sum is -1/12. Those are unassailable facts. What you are trying to insist to me in strident tones is that one way of adding infinitely many things together is REAL and the other is a SHAM. Everybody knows that when you go out into the real world and add things together infinitely many times, you get the former, not the latter. Right?
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