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...
12 KB (1,638 words) - 00:46, 12 February 2024
Sprague–Grundy theorem (section Nimbers)
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...
20 KB (3,353 words) - 17:19, 15 August 2023
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...
5 KB (686 words) - 08:06, 25 April 2024
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...
5 KB (740 words) - 21:18, 29 August 2023
military decorations State decoration Army-Navy "E" Award Medal inflation "Nimber 1348.33, Volume 3" (PDF). Defense Technical Information Center. United States...
51 KB (1,330 words) - 03:00, 6 August 2024
Ordinal arithmetic (section Nimber arithmetic)
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...
36 KB (4,944 words) - 13:10, 12 July 2024
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...
2 KB (285 words) - 12:11, 6 July 2021
expense of continuity. Interpreted as nimbers, a game-theoretic variant of numbers, ordinals can also be combined via nimber arithmetic operations. These operations...
47 KB (6,717 words) - 10:52, 24 July 2024
Nimber addition is the exclusive or of nonnegative integers in binary representation. This is also the vector addition in ( Z / 2 Z ) 4 {\displaystyle...
31 KB (3,346 words) - 00:37, 8 August 2024
Combinatorial game theory (section Nimbers)
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...
24 KB (3,198 words) - 07:21, 1 February 2024