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 Aug 23 comment Is there a name for complex numbers over affinely extended reals? @Hurkyl agreed, but what's the usual name (or symbol) for such set? Aug 23 comment Is there a name for complex numbers over affinely extended reals? @Mariano Suárez-Alvarez And inverse Mellin tranform uses the both in one formula: upload.wikimedia.org/math/5/4/a/… Aug 23 comment Is there a name for complex numbers over affinely extended reals? @Mariano Suárez-Alvarez Look for instance at the Wiki article about Forier transform. It uses both complex numbers and signed infinities a lot: en.wikipedia.org/wiki/Fourier_transform Aug 23 comment Motivation for different mathematics foundations ZC? Did you mean ZF? Aug 22 comment Is there a formulaic way to go from $\sum_{k=1}^{n} \frac{1}{k}$ back to $n$? Why is the downvote? Aug 21 comment Zero to the zero power - Is $0^0=1$? The second "general rule" is wrong. It is correct only for positive numbers. Aug 13 comment Why the number of all reals is $2^{\aleph_0}$ and not ${\aleph_0}^{\aleph_0}$? But I think in this system one can define "sub-$\Omega$" numbers which would play the role of natural numbers Aug 13 comment Why the number of all reals is $2^{\aleph_0}$ and not ${\aleph_0}^{\aleph_0}$? @Asaf Karagila The smallest number which can be written using such "decimal" expansion using positions and base up to $\Omega$ will be, well... $\frac{1}{{(\Omega+1)}^{\Omega}-1}$. It is not real though indeed. Aug 13 comment Why the number of all reals is $2^{\aleph_0}$ and not ${\aleph_0}^{\aleph_0}$? @Asaf Karagila I am actually talking about a theory where it is not based on bijections. I have just applied brute force of a numerical sustem of infinite numbers (reals+infinites) so to find the quantity of reals and these are the results I obtained (using the notion of "smallest real" which apparently exists in such system). Aug 13 comment Why the number of all reals is $2^{\aleph_0}$ and not ${\aleph_0}^{\aleph_0}$? @Asaf Karagila I meant the system which is not invariant against addition Aug 13 comment Why the number of all reals is $2^{\aleph_0}$ and not ${\aleph_0}^{\aleph_0}$? So can it be that in a more precise system of infinite number these two quantities are different? Jul 7 comment What are the negative-dimentional n-sphere and n-cube? @Eric Wofsey but does it obey the above formulas? Jun 18 comment Example of a function that has fractional derivatives of order less than 1 but not 1 With s=1 it is differentiable? Jun 5 comment Solutions of sixth order polynomial equations In what form do u want the solution - series, special functions, limit or anything else? Some computer algebra systems already have root of a polynomial as a built-in function. May 19 comment Why is $\lim_{(x,y)\to(0,0)}\frac yx \ne 0$? It is discontinuous at (0,0). May 19 comment Why is $\lim_{(x,y)\to(0,0)}\frac yx \ne 0$? Depending on your definition of the limit with two variables, it can be 0. May 18 comment Can the Riemann Zeta derivative be expressed in terms of Riemann Zeta? The problem with your addition part is also that polygamma is not defined for non-integer indexes as well. May 17 comment Concerning Hurwitz Zeta function, how to prove the following identity? May 17 comment Concerning Hurwitz Zeta function, how to prove the following identity? Can the F.3.6 integrals be represented in closed form? May 17 comment Concerning Hurwitz Zeta function, how to prove the following identity? I've got the following: $$\int_0^{\infty } \frac{1}{4} (\coth (\pi t)-1) \left(a^2+t^2\right)^{-\frac{s}{2}} \left(2 \tan ^{-1}\left(\frac{t}{a}\right) \cos \left(s \tan ^{-1}\left(\frac{t}{a}\right)\right)-\log \left(a^2+t^2\right) \sin \left(s \tan ^{-1}\left(\frac{t}{a}\right)\right)\right) \, dt$$ using Mathematica.