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Gonshor, Harry
Length of surreal product ★
Author(s): Gonshor
Conjecture Every surreal number has a unique sign expansion, i.e. function
, where
is some ordinal. This
is the length of given sign expansion and also the birthday of the corresponding surreal number. Let us denote this length of
as
.
![$ f: o\rightarrow \{-, +\} $](/files/tex/70df8f7b1ba4ff48d933bb62e8ec5290ad07a83b.png)
![$ o $](/files/tex/edb7612a8d6e29df825595761e763255474053d0.png)
![$ o $](/files/tex/edb7612a8d6e29df825595761e763255474053d0.png)
![$ s $](/files/tex/5161d8e30b9db389fca68be55f99b5f9e0f8ea7c.png)
![$ \ell(s) $](/files/tex/156ccbe910e8f543b887e2294bcd5a450e454caf.png)
It is easy to prove that
What about
?
Keywords: surreal numbers
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