- 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...
- 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...
- 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...
- are
known as
nimbers. The Sprague–Grundy
theorem states that
every impartial game
under the
normal play
convention is
equivalent to a
nimber. The "smallest"...
-
military decorations State decoration Army-Navy "E"
Award Medal inflation "
Nimber 1348.33,
Volume 3" (PDF).
Defense Technical Information Center.
United States...
-
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...
-
expense of continuity.
Interpreted as
nimbers, a game-theoretic
variant of numbers,
ordinals can also be
combined via
nimber arithmetic operations.
These operations...
-
Nimber addition is the
exclusive or of
nonnegative integers in
binary representation. This is also the
vector addition in ( Z / 2 Z ) 4 {\displaystyle...
