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Jul
29
comment Can the numbers $2^m 3^n$ have an infinitely long arithmetic sequence?
See it's not so easy? Dirichlet's theorem was my motivation for this problem. As for the comments above, proving the natural density is 0 might also be hard.
Jul
25
comment Can $O(\sqrt{x})$ be considered $o(x)$?
@user251257 Oh my. What an important question. I guess $\boxed{x \to \infty}$, but $x \to 0$ could be important.
Jul
19
comment Product of complex numbers $m+in$ with $0 < m,n \leq N$
@zardo if you can find Stirling approximation in that case then please write an answer
Jul
18
comment Explaining Mathematical Modelling to a nonmathematician
have you considered Math Educators Stackexchange
Jul
9
comment How prove this inequality $(1+\frac{1}{16})^{16}<\frac{8}{3}$
@StevenStadnicki thanks I redid it from scratch
Jul
9
comment Extending 2-adic valuation to real numbers
@Wojowu I now agree. You can define 2-adic norms over any extension over $\mathbb{Q}$. This includes algebraic extensions like $\mathbb{Q}(\sqrt{7})_2$ or $[\mathbb{Q}[x]/(x^3 - x - 1)]_2$ and transcendental extensions like $\mathbb{Q}(\pi)$. Then $\mathbb{R}$ contains all of these. This is even beigger than the algebraic closure $\overline{\mathbb{Q}} \cap \mathbb{R}$ containing all real algebraic extensions.
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
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
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
25
comment Integral relations in Fricke and Klein
@glebovg I think they want to give you the option of not awarding any bounty at all. In the case nobody answers the way you wanted.
Jun
24
comment Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse?
I really like your numerical approach to this problem.
Jun
24
comment Arnold Trivium Problem 39
@Potato since the Gauss integral does not change under deformations, we can deform $A$ into a straight line or (even easier) flatten $B$ into a circle, where we going around twice. Then the integral might be doable by hand. This is line when we integrate complex functions using Cauchy Residue Formula.
Jun
24
comment Arnold Trivium Problem 39
@Potato I wouldn't dream of doing the integrals by hand... unless you truly enjoy long and tedious integrals :-)
Jun
24
comment Arnold Trivium Problem 39
I have to step away, but I can do a numerical calculation... just to see!
Jun
24
comment Arnold Trivium Problem 39
e.g. Gauss Linking Number Revisited (Ricca + Nipoti) Journal of Knot Theory and Its Ramifications
Jun
23
comment Integral relations in Fricke and Klein
@glebovg i added more details... why didn't you give me the 100?