Ordinal arithmetic

In the mathematical field of set theory, ordinal arithmetic includes binary operations on ordinal numbers such as addition, multiplication, and exponentiation. Each can be defined in two different ways: either by constructing an explicit well-ordered set that represents the result of the operation or by using transfinite recursion. In addition to these standard operations for ordinals, there are also the "natural" arithmetic operations, which are usually described using the Cantor normal form for ordinals, and nimber operations.

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