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stats | profile views | 4,721 |
Apr 22 |
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Surreal numbers, ultrapowers of $\Bbb R$, ordinal-valued functions and the slow-growing hierarchy
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Apr 22 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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Are hyperreal numbers isomorphic to formal power series?
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Jan 24 |
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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? |
Jan 24 |
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Are hyperreal numbers isomorphic to formal power series?
Oh, it seems you misunderstood me! In my question I meant $\omega$ to be infinite, as usually in non-standard analysis it is postulated to be equal to the first ordinal $\omega$. |
Jan 24 |
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Are hyperreal numbers isomorphic to formal power series?
"No, you can form a hypperreal $\sin ω$". - hmm, I am curious, will it be an infinitesimal? |
Jan 24 |
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Are hyperreal numbers isomorphic to formal power series?
I think the last comment is very valuable, can you please add this to the answer? |