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Revision as of 09:56, 5 June 2020
Ordinals are an extension of the natural numbers. Ordinals can be used to describe the order type of a set. The order type of the natural numbers is the first infinite ordinal, . Ordinals can be added and multiplied. The sum of two ordinals
and
is the ordinal that describes the order type of a set with order type a concatenated with one of order type b. Warning! Ordinal addition is not commutative. For example
, while
.
Every ordinal characterizes the order type of the ordered ordinals less than it. For example, has order type
.
The smallest ordinal that can't be constructed from by addition, multiplication, and exponentiation is
, the first fixed point of the map
.