# 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 .

It is easy to prove that

What about

?

Keywords: surreal numbers