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13
votes
2answers
557 views

Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers?

Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers? Which of their properties and relations (e.g. usual trig identities) will still ...
9
votes
1answer
912 views

Surreal numbers vs. non-standard analysis

What is the relationship between the surreal numbers and non-standard analysis? In particular, is there a transfer principle for surreal numbers they way there is for NSA? A specific situation in ...
9
votes
0answers
437 views

Characterizing the surcomplex numbers

Conway showed that the Field of surreal numbers ("${\bf No}$") is the maximal totally ordered Field. Later Jacob Lurie showed that the Group of all partizan games ${\bf Pg}$ is the universally ...