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Mar
25
comment Has anybody ever considered “full derivative”?
@Hayden I am about introducing one element, $\varepsilon$, similarly to how complex $i$ introduced. One can argue such system would be undefinable, but then complex numbers are also undefinable because $i$ is indistinguishable from $-i$. By the way, in the context of surreals, hyperreal numbers can be considered a subfield $No(\omega)$. Then this $\omega$ has definite meaning: it is considered equal to the first infinite ordinal.
Mar
25
comment General form for series coefficient of Taylor series expansion of $(x+1)^{1/x}$
@mickep around zero
Mar
25
comment Has anybody ever considered “full derivative”?
@Hayden in usual non-standard analysis they usually do not introduce distinguished elements $\varepsilon$ and $\omega$, thus they cannot uniquely define full derivative.
Mar
25
comment Has anybody ever considered “full derivative”?
@kjetil b halvorsen this is not q-derivative, totally different thing.
Mar
25
comment Why hyperreal numbers are built so complicatedly?
Thanks for pointing out the Levi-Civita field
Mar
23
comment Who discovered the first explicit formula for the n-th prime?
It is not elementary functions.
Mar
17
comment Why hyperreal numbers are built so complicatedly?
Why is the downvote?
Mar
15
comment What function satisfies the following equation?
What if additional condition is imposed, that isfunction $f(x+\pi/4)e^{-x}\Gamma(x/\pi +1/4)$ is even?
Mar
10
comment What function satisfies the following equation?
This is Great!!! Thank you very much!
Mar
10
comment What exactly *is* the Riemann zeta function?
The latest identity is wrong :-(
Mar
8
comment Can such function exist?
What about the second part of the question?
Mar
8
comment Can such function exist?
What about the second part?
Mar
5
comment What are the negative-dimentional n-sphere and n-cube?
@MvG if distance is defined on a fractal (for instance, on Serpinsky triangle en.wikipedia.org/wiki/Hausdorff_dimension#mediaviewer/… ), then all points equally distant from a given one form a sphere.
Mar
5
comment What are the negative-dimentional n-sphere and n-cube?
@Yuval Filmus what non-integer positive dimentional space and n-sphere is clear: a fractal. But what about negative?
Mar
4
comment Solving $\cos x=x$
math.stackexchange.com/questions/227317/explaining-cos-infty/…
Mar
4
comment What is the solution of cos(x)=x?
math.stackexchange.com/questions/227317/explaining-cos-infty/…
Mar
4
comment Explaining $\cos^\infty$
@GDumphart you can check it. If you eliminate arctan and tan, the result changes, becomes wrong. It you know other ways to simplify it, you are welcome.
Mar
4
comment Solving $2x - \sin 2x = \pi/2$ for $0 < x < \pi/2$
Why the index of the Bessel functions is not equal to the argument in your expression?
Mar
4
comment Solving $2x - \sin 2x = \pi/2$ for $0 < x < \pi/2$
By the way, the formula $$\sum_{n=1}^\infty \frac{2J_n(n)}{n} \sin(\pi n/2)$$ works for Dottier number.
Mar
4
comment What is the solution of cos(x)=x?
How having closed-form expression is related to being transcedential?