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Results tagged with surreal-analysis
Search options questions only
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user 10059
6
votes
1
answer
488
views
In surreal numbers, what are the main difficulties so far in defining integration?
I know, there were several (including unsuccessful) attempts at defining integration on surreal numbers, so I am asking for a good summary of what have been the main difficulties so far.
Particularly, …
- 10.1k
0
votes
0
answers
117
views
Can one represent divergent integrals or germs at infinity with surreal numbers?
I have been disliking the theory of surreal numbers for a while, but let's test it.
So, we have a set of divergent improper integrals of continuous functions with the following ordering: $\int_0^\inft …
- 10.1k
0
votes
0
answers
142
views
Why is the property of linearity against an infinitely-large factor considered essential for...
Why the property $(b)$ in Proposition 14 in this paper on surreal integration is considered essential?
The Proposition lists the desired properties of the surreal integration, and among others lists t …
- 10.1k
-1
votes
1
answer
268
views
Why is it said that all surreal numbers with birthdate $<\omega_1$ are isomorphic to a Hardy...
In this answer I have encountered with the following statement:
Assuming CH, every maximal Hardy field is isomorphic to
$(\bf{No}(\omega_1), \partial_{\omega_1})$, where $\bf{No}(\omega_1)$
is the s …
- 10.1k