Reputation
2,025
Top tag
Next privilege 2,500 Rep.
Create tag synonyms
Badges
1 9 22
Impact
~34k people reached

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?
Done: math.stackexchange.com/questions/1287008/…
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.