What physicists mean when they say 1+2+3+... = -1/12pic.twitter.com/Noj5pEf1Ym
PhD student of Theoretical Particle Physics @UCIrvine l @NSF Fellow l Physics & Math Animations l Patreon: https://www.patreon.com/inertialobserver …
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What physicists mean when they say 1+2+3+... = -1/12pic.twitter.com/Noj5pEf1Ym
Right but that’s the point.. I’m not taking the limit.. everything is finite until the very last step where the divergence is clearly isolated to one term
I believe any divergent series can be written as f(ε) + o(g(ε))+ constant Where f(ε) ⇒∞ as ε⇒0
That’s Riemann’s reordering theorem, and it applies to changing the order of terms in an infinite series. Renormalization is procedure with a unique result.. Terrance Tao wrote at length about it
Reordering is applied only for alternating series that converges conditionally..
Right and conclusions about divergent series only apply to divergent terms.. just because 1/x diverges at x=0 doesn’t mean its meaning less to talk about it everywhere else
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