What physicists mean when they say 1+2+3+... = -1/12pic.twitter.com/Noj5pEf1Ym
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The RHS of eq (3) diverges when ε⇒0
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
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I believe any divergent series can be written as f(ε) + o(g(ε))+ constant Where f(ε) ⇒∞ as ε⇒0
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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
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