Ordinal exponentiation

Ordinal exponentiation extends multiplication to ordinal numbers, which measure the sizes of well-ordered sets. For example, raising an ordinal to a power involves repeatedly applying the ordinal to itself according to the exponent, similarly to how regular exponents represent repeated multiplication. Specifically, ordinal exponentiation is defined recursively: an ordinal raised to zero equals 1, while for a successor ordinal, it equals the base multiplied by the base raised to the previous exponent. For limit ordinals, it’s defined as the limit (or supremum) of the exponentiation results for all smaller exponents. This process captures increasingly complex notions of 'size' and order.