nimbers造句

• Except for the fact that nimbers form a characteristic 2.
• The "'minimum excludant "'operation is applied to sets of nimbers.
• For all natural numbers, the set of nimbers less than form the Galois field of order.
• In particular, this implies that the set of finite nimbers is isomorphic to the direct limit as of the fields.
• The nimber multiplicative inverse of the nonzero ordinal is given by, where is the smallest set of ordinals ( nimbers ) such that
• The smallest algebraically closed field of nimbers is the set of nimbers less than the ordinal, where is the smallest infinite ordinal.
• The smallest algebraically closed field of nimbers is the set of nimbers less than the ordinal, where is the smallest infinite ordinal.
• By the induction hypothesis, all of the options are equivalent to nimbers, say G _ i \ approx * n _ i.
• In 2007, Julien Lemoine and Simon Viennot introduced an algorithm based on the concept of nimbers to accelerate the computation, reaching up to 32 spots.
• If is 2 stones, the player to move can leave 0 or 1 stones, giving the nimber 2 as the mex of the nimbers } }.
• For example, the game * 2 + * 3, where the values are nimbers, has value * despite each player having more options than simply moving to 0.
• In general, the player to move with a pile of stones can leave anywhere from 0 to stones; the mex of the nimbers } } is always the nimber.
• Also, the concept of nimbers isn't made clear enough in the article for me .  & # 9742; 20 : 04, 2 March 2015 ( UTC)
• If we change the game so that the player to move can take up to 3 stones only, then with stones, the successor states have nimbers } }, giving a mex of 0.
• The nimbers are the ordinal numbers endowed with a new "'nimber addition "'and "'nimber multiplication "', which are distinct from ordinal addition and ordinal multiplication.
• In mathematics, the "'nimbers "', also called "'Grundy numbers "', are introduced in combinatorial game theory, where they are defined as the values of nim heaps.
• Normal play Nim ( or more precisely the system of nimbers ) is fundamental to the Sprague Grundy theorem, which essentially says that in normal play every impartial game is equivalent to a Nim heap that yields the same outcome when played in parallel with other normal play impartial games ( see disjunctive sum ).
• This subfield is not algebraically closed, since no other field ( so with not a power of 2 ) is contained in any of those fields, and therefore not in their direct limit; for instance the polynomial, which has a root in, does not have a root in the set of finite nimbers.
• For stones, the nimbers of the successor states of 2, 3, and 4 stones are the nimbers 2, 3, and 0 ( as we just calculated ); the mex of the set of nimbers } } is the nimber 1, so starting with 5 stones in this game is a win for the first player.
• For stones, the nimbers of the successor states of 2, 3, and 4 stones are the nimbers 2, 3, and 0 ( as we just calculated ); the mex of the set of nimbers } } is the nimber 1, so starting with 5 stones in this game is a win for the first player.