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   denotes the nth term in the fundamental sequence of ω. This in turn allows the precise definition of a function which grows more rapidly than any function in the series. 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.