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...

an ordinal number in the infinite generalization, or alternatively as a nimber, the value of that one-heap game in an algebraic system whose addition operation...

game under the normal play convention is equivalent to a nimber. The representation of this nimber can change from game to game, but every possible state...

gives the nimber for this case. If n is 2 stones, the player to move can leave 0 or 1 stones, giving the nimber 2 as the mex of the nimbers {0, 1}. In...

operations, there are also the "natural" arithmetic of ordinals and the nimber operations. The sum of two well-ordered sets S and T is the ordinal representing...

military decorations State decoration Army-Navy "E" Award Medal inflation "Nimber 1348.33, Volume 3" (PDF). Defense Technical Information Center. United States...

expense of continuity. Interpreted as nimbers, a game-theoretic variant of numbers, ordinals can also be combined via nimber arithmetic operations. These operations...

position in a partisan game can have a nimber as its value, or else the game would be impartial. However, some nimbers can still occur as the values of game...

Nimber addition is the exclusive or of nonnegative integers in binary representation. This is also the vector addition in ( Z / 2 Z ) 4 {\displaystyle...

way are known as nimbers. The Sprague–Grundy theorem states that every impartial game is equivalent to a nimber. The "smallest" nimbers – the simplest and...