Ordinals

Ordinals are a type of number that measure position in a series or set, such as the "5th runner in a race" or "3rd line from the right". They are used in googology to denote transfinite numbers such as omega (ω), the first transfinite ordinal, or Omega (Ω / ω1), the first uncountable ordinal. They may be used as indexes in the subscript of the fast growing hierarchy, so that an expression like  can be defined as being equal to , where. Larger ordinals can be used to define faster growing functions still, with the discovery of large countable ordinals being of paramount interest to many contemporary googologists.