**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 .

It is easy to prove that

What about

?

This is strongly conjectured to be true by Gonshor in [Gon86]. There is an easy way to prove that

## Bibliography

*[Gon86] Harry Gonshor, An Introduction to the Theory of Surreal Numbers, Cambridge University Press, Cambridge, 1986.

* indicates original appearance(s) of problem.