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Jul
7
revised Proof that derivative of Hurwitz Zeta by the first argument is not expressable in terms of Hurwitz Zeta
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Jul
7
comment Proof that derivative of Hurwitz Zeta by the first argument is not expressable in terms of Hurwitz Zeta
@Henry Cohn, Hurwitz Zeta, generalized Bernoulli polynomials, polylogarithm, polygamma. All expressable through each other.
Jun
9
asked Can these integrals be represented in closed form?
Apr
22
revised Surreal numbers, ultrapowers of $\Bbb R$, ordinal-valued functions and the slow-growing hierarchy
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Apr
22
comment Are there any standard analysis facts that can be proven or arrived only by means of non-archimedean extensions of reals and non-standard analysis?
@Andreas Blass following your logic, there is no theory at all that can provide new results compared to the arithmetic of natural numbers: any theory (even outside of ZFC) can be written in symbols encoded with natural numbers and operations over them. Thus no theory can give any insight beyond what arithmetic of natural numbers provides.
Apr
5
comment Are there any standard analysis facts that can be proven or arrived only by means of non-archimedean extensions of reals and non-standard analysis?
@M T obviously, complex numbers are also in ZFC, yet they provide a lot of new results to real analysis.
Apr
5
revised Are there any standard analysis facts that can be proven or arrived only by means of non-archimedean extensions of reals and non-standard analysis?
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Apr
5
asked Are there any standard analysis facts that can be proven or arrived only by means of non-archimedean extensions of reals and non-standard analysis?
Mar
28
revised Obtaining graphics of functions in non-standard analysis
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Mar
28
revised Obtaining graphics of functions in non-standard analysis
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Mar
28
asked Obtaining graphics of functions in non-standard analysis
Jan
26
revised Analysing functions on zero-length intervals and super-small values
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Jan
26
revised Analysing functions on zero-length intervals and super-small values
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Jan
26
revised Analysing functions on zero-length intervals and super-small values
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Jan
26
asked Analysing functions on zero-length intervals and super-small values
Jan
25
comment Are hyperreal numbers isomorphic to formal power series?
@Noah S I think in $No(\omega_1)$ there is. But I still would like a clarification.
Jan
24
comment Are hyperreal numbers isomorphic to formal power series?
Actually to be more precise I was referring to Conway's $No$ ohio.edu/people/ehrlich/Unification.pdf
Jan
24
comment Are hyperreal numbers isomorphic to formal power series?
So if we take $\omega$ as infinite element, there are formal power series (like $\sin \omega$) which are not hyperreals apparently, so the power series seems to be a bigger set than hyperreals?
Jan
24
revised Are hyperreal numbers isomorphic to formal power series?
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Jan
24
comment Are hyperreal numbers isomorphic to formal power series?
So $\sin (1/\omega)=\sin \varepsilon$ is definitely a hyperreal and infinitesimal, but what about $\sin \omega$ then?