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visits | member for | 4 years, 5 months |
seen | 2 hours ago | |
stats | profile views | 4,657 |
Mar 28 |
revised |
Obtaining graphics of functions in non-standard analysis
edited body |
Mar 28 |
revised |
Obtaining graphics of functions in non-standard analysis
added 2 characters in body |
Mar 28 |
asked | Obtaining graphics of functions in non-standard analysis |
Mar 15 |
asked | What special role plays the function $\pi^{\frac x\pi}$ in analysis? |
Jan 26 |
revised |
Analysing functions on zero-length intervals and super-small values
added 7 characters in body |
Jan 26 |
revised |
Analysing functions on zero-length intervals and super-small values
added 37 characters in body |
Jan 26 |
revised |
Analysing functions on zero-length intervals and super-small values
added 4 characters in body |
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?
added 10 characters in body |
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? |
Jan 24 |
comment |
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 |
comment |
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 |
comment |
Are hyperreal numbers isomorphic to formal power series?
I think the last comment is very valuable, can you please add this to the answer? |
Jan 24 |
accepted | Are hyperreal numbers isomorphic to formal power series? |
Jan 24 |
comment |
Are hyperreal numbers isomorphic to formal power series?
If the hyperreals are bigger, can we say that the formal power series (or converging power series or analytic functions) are isomorphic to a subset of hyperreals? |
Jan 24 |
comment |
Are hyperreal numbers isomorphic to formal power series?
By the way, $\sin \omega$ does belong to the formal power series but does not to hyperreals, is this wrong or correct? |
Jan 24 |
revised |
Are hyperreal numbers isomorphic to formal power series?
deleted 6 characters in body |