Inverse Element for Surreal Number

Abstract

Conway’s surreal numbers have a fascinating algebraic structure, which we try to formalise in the Mizar system. In this article, building on our previous work establishing that the surreal numbers fulfil the ring properties, we construct the inverse element for any non-zero number. For that purpose, we formalise the definition of the inverse element formulated in Section Properties of Division of Conway’s book. In this way we show formally in the Mizar system that surreal numbers satisfy all nine properties of a field.