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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
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
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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?
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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?
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?
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