john mangual
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 Jul 6 answered Sum: $1-2+3-4+5-6+…$ Jul 6 revised Extending 2-adic valuation to real numbers added 810 characters in body Jul 6 revised Extending 2-adic valuation to real numbers added 238 characters in body Jul 6 revised Extending 2-adic valuation to real numbers added 238 characters in body Jul 6 revised Extending 2-adic valuation to real numbers added 223 characters in body Jul 6 answered Extending 2-adic valuation to real numbers Jun 29 revised Is there something between summation and integration? added 499 characters in body Jun 29 comment Is there something between summation and integration? this is answering a very different question actually, but it might be of interest Jun 29 answered Is there something between summation and integration? Jun 28 comment How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization @AsafKaragila I specify this was done with zeta function regularization. Would it be more precise to ask for the analytic continuation $\zeta(0)$ ? Jun 28 comment How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization Could you prove Ramanujan summation as Euler-Maclaurin to 1st order? Jun 28 comment How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization hmm? that seems plausible that $\sum (0+2) = \sum (1+1)$ and yet $\sum (0+2) = 2 \sum 1$. Jun 28 comment How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization @AsafKaragila this false statement has its own wikipedia article Jun 28 revised How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization added 460 characters in body Jun 28 asked How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization Jun 28 comment What we get if we add 1/2 infinite times @Ant There is nothing wrong with this kind of experimentation. Euler did it, Physicists do it routinely (via their lack of rigour). He just needs to understand these series come with at the expense of associativity. We can't invoke $(a+b)+c = a + (b+c)$ infinitely many times and always get away with it. Watch his parentheses carefully. Jun 28 comment What we get if we add 1/2 infinite times @Ant his question seems to be whether these divergent series identities can be found via elementary rearrangements. Jun 28 revised Proof $\{(x,y,z)|4x^2+9y^2+16z^2<1\}$ is an open set added 463 characters in body Jun 28 answered What we get if we add 1/2 infinite times Jun 28 answered Proof $\{(x,y,z)|4x^2+9y^2+16z^2<1\}$ is an open set