Ordinal numbers | Finite fields | Combinatorial game theory
Nimber
In mathematics, the nimbers, also called Grundy numbers, are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim. The nimbers are the ordinal numbers endowed with nimber addition and nimber multiplication, which are distinct from ordinal addition and ordinal multiplication. Because of the Sprague–Grundy theorem which states that every impartial game is equivalent to a Nim heap of a certain size, nimbers arise in a much larger class of impartial games. They may also occur in partisan games like Domineering. Nimbers have the characteristic that their Left and Right options are identical, following a certain schema, and that they are their own negatives, such that a positive ordinal may be added to another positive ordinal using nimber addition to find an ordinal of a lower value. The minimum excludant operation is applied to sets of nimbers. (Wikipedia).
