<P> Surreal numbers: A number system that includes the hyperreal numbers as well as the ordinals . The surreal numbers are the largest possible ordered field . </P> <P> Computable number: A real number whose digits can be computed using an algorithm . </P> <P> Definable number: A real number that can be defined uniquely using a first - order formula with one free variable in the language of set theory . </P>

Natural numbers whole numbers integers rational numbers irrational numbers real numbers