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Results tagged with surreal-numbers
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user 28128
For questions about the surreal numbers, which are a real-closed ordered proper-class-sized field that contains both the real numbers and the ordinal numbers. Thus they contain both infinite numbers (including the ordinals, but also infinite numbers like ω-1 and sqrt(ω)) and infinitesimal numbers (like 1/ω). They can also be identified with a subclass of two-player partisan games.
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Surreal numbers vs. non-standard analysis
The real question as far as "ordinary mathematics" is concerned is whether there is a set-size surreal extension of the reals useful in doing analysis, and that as a very minimum admits a sine functio …
- 16.6k
5
votes
Accepted
Are there results unique to non-standard analysis or surreal numbers that have not been reco...
The key paper in this area is Henson and Keisler:
C. W. Henson and H. J. Keisler, On the strength of nonstandard
analysis}, J. Symbolic Logic, 51 (1986), no. 2, 377-386.
The elaborate on the point y …
- 16.6k
3
votes
In hyperreal field, can ln(ε) and ln(ω) be expressed as infinite sums?
For positive $\epsilon$, the expression $\ln \epsilon$ will be equal to its power series at $x=1$ (in the $\delta, N$ sense).
To help avoid any misunderstanding that may arise for readers of this ques …
- 16.6k
5
votes
What's wrong with the surreals?
A quick search indicates that Peano axioms are not mentioned on this page. It seems reasonable to mention that there does not seem to be a good notion of natural number in the surreals that would sati …
- 16.6k