Timeline for Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| May 30, 2013 at 19:09 | comment | added | Gerald Edgar | For trig functions, see mathoverflow.net/questions/91337 | |
| May 30, 2013 at 18:53 | answer | added | J. M. isn't a mathematician | timeline score: 1 | |
| May 29, 2013 at 0:57 | vote | accept | OlegK | ||
| May 25, 2013 at 17:44 | history | edited | OlegK |
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| May 25, 2013 at 5:23 | comment | added | Jason Rute | I will also comment that this is also the area of model theory over metric structures. You should be able to get hyperfinite nonstandard models of the real and complex numbers with these functions by taking ultraproducts. What I can't remember is (1) which properties are preserved by ultraproducts of metric structures, and (2) how exactly ultraproducts of $\mathbb{R}$ and $\mathbb{C}$ relate to surreal numbers. For example, is the ultraproduct $\prod_I \mathbb{R}$, where I is a proper class, isomorphic to the surcomplex numbers? I'll leave these questions to the experts on this subject. | |
| May 25, 2013 at 5:11 | answer | added | Alex Becker | timeline score: 6 | |
| May 25, 2013 at 5:07 | comment | added | Jason Rute | The set theory tag would be better as a logic tag. This is really the area of nonstandard analysis. | |
| May 25, 2013 at 3:25 | history | asked | OlegK | CC BY-SA 3.0 |