I went full @3blue1brown and used Manim to illustrate the proof of the Geometric Series formulapic.twitter.com/c3kVy63SIh
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Yes. But you have to make that assumption, which was not visible in what you wrote or animated. iirc, the -1/12 problem goes quite a bit deeper than 1-1+1... not converging in the "for all epsilon..."sense. Indeed, I am being nit-picky, but that's math, right?
The heuristic doesn't go any deeper than that. All manipulations of that fashion rely on a non-traditional form of convergence(e.g. Cesaro)..I covered the proper way to consider the summation in the linked tweet yes, that's math but this is also twitterhttps://twitter.com/InertialObservr/status/1083153666431807488?s=20 …
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well, 1-1+1... is Cesaro-summable, 1+2+3+... is not. To give a proper meaning to the sum being equal to -1/12, you have to use an analytic continuation of the zeta function, right? Just saying it woul've been nice to add the assumpton, to not have the same end as a certian video.
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No, the zeta function sum formula only makes sense for Re(s) > 1 .. the fact this should apply to -1 is unfounded To “make sense” of the sun you need to talk about regularized sums
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