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Topic: Nimbers

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	Good Math, Bad Math : Surreal Nimbers: No, that's not a typo!
		The trick to creating nimbers is going to be using an ordinal process where we don't distinguish between left and right sets in the nimbers, but we use the idea of the corresponding surreals to define things like ≤.
		So for any two nimbers A and B, the addition operation is really bitwise exclusive-or of the binary expansion of the number.
		In nimber multiplication, the nimber product of two distinct Fermat 2-powers is their product in the normal surreal number field.
	scienceblogs.com /goodmath/2007/04/surreal_nimbers_no_thats_not_a_1.php (1547 words)

	Nimber
		The proper class of nimbers is the proper class of ordinals endowed with a new nimber addition and nimber multiplication, which are distinct from ordinal addition and ordinal multiplication.
		Except for the fact that nimbers form a proper class and not a set, the class of nimbers determines an algebraically closed field of characteristic 2.
		Just as in the case of nimber addition, there is a means of computing the nimber product of finite ordinals.
	www.ebroadcast.com.au /lookup/encyclopedia/ni/Nimber.html (364 words)

	YourArt.com >> Encyclopedia >> nimber (Site not responding. Last check: )
		In mathematics, the proper class of nimbers (occasionally called Grundy numbers) is introduced in combinatorial game theory, where they are defined as the values of nim heaps, but arise in a much larger class of games because of the Spragueâ“Grundy theorem.
		It is the proper class of ordinals endowed with a new nimber addition and nimber multiplication, which are distinct from ordinal addition and ordinal multiplication.
		Nimber addition (also known as nim-addition) can be used to calculate the size of a single heap equivalent to a collection of heaps.
	www.yourart.com /research/encyclopedia.cgi?subject=/nimber (432 words)

	Sprague–Grundy theorem - Encyclopedia, History, Geography and Biography
		In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game is equivalent to a nimber.
		In the case of a game whose positions (or summands of positions) are indexed by the natural numbers (for example the possible heap sizes in nim-like games), the sequence of nimbers for successive heap sizes is called the nim-sequence of the game.
		A nimber is a special game denoted *n for some ordinal n.
	www.arikah.com /encyclopedia/Sprague-Grundy_theory (626 words)

	[No title]
		This is of course possible (because all nimbers less than the nimber of the position are achievable, including 0).
		That is, that the nimber of the join of two games is just a function of the nimbers of the two parts.
		For one thing, it's not even clear that the nimber of the join is even a function of the nimbers of the two games being joined.
	www.cs.cmu.edu /afs/cs/academic/class/15859-f01/www/notes/sleator-nim-notes.txt (1214 words)

	Untitled Document (Site not responding. Last check: )
		With impartial games, the concept of nimbers, and nimber addition can be used.
		A Nimber is used to describe the number of moves in a particular impartial game.
		The goal of this research is to classify common nimbers so that they could be used with higher nimbers to create simpler nimbers when looking at multiple games.
	www.personal.psu.edu /users/l/f/lfg112/research.htm (527 words)

	Good Math, Bad Math : The Strangeness of Nimber Addition
		The way that we did it was iterative: take a set of existing nimbers that exist at ordinal stage N, and use a simple procedure to try to create as many nimbers as we could by adding pairs of stage-N nimbers.
		Doing the addition is basically asking what's the nimber that models a single pile game that has exactly the same winners (assuming perfect players) as the two-pile game N+M? No, that is too weak, after all there are only two options for who wins in a single game.
		What I think you mean is: what's the nimber such that a single pile of that size can replace a pair of N and M piles in any other Nim game, without changing the outcome.
	scienceblogs.com /goodmath/2007/05/the_strangeness_of_nimber_addi_1.php (3724 words)

	Contents
		We restrict ourselves to a few very simple applications.
		``Nimbers'' and factorization techniques for polynomials are covered as special topics.
		Basic topics, such as check matrices, generator matrices, and syndrome decoding are covered.
	web.usna.navy.mil /~wdj/book/node1.html (878 words)

	Number theory files for David Eppstein
		This notebook for Mathematica 2.2/Macintosh (also available in HTML format) describes and implements a number of different algorithms for representing rational numbers as sums of distinct unit fractions.
		Conway's nimbers (used in combinatorial game theory) form an infinite field of characteristic two, with a natural binary representation in which truncation to a fixed number of bits produces finite subfields GF[2^2^k].
		The algorithms in this file implement nimber multiplication, square root, and other functions, using O(k 3^k) bit operations.
	www.ics.uci.edu /~eppstein/numth (464 words)

	Pa lottery ticket
		pa lottory nimbers, pa state lottery is the same as winning numbers for mega millions lotterypa stte lotter pa daily lottery result, pa daily rottely resilt search.
		Our website sells current pa lottery result and current pa lotarie rrsult or pa lottery daily number, pa rottelie daily nimber.
		pa rottarie drawing and lottery number pa raffle, lotarie nimber pa raffle, pa past lottery includes pa past rottelie pa lottery scratch off game, pa rottorie scratch off game products.
	www.freewebs.com /dilevery/pa-lottery-ticket.html (313 words)

	diasonics part nimbers ► Ultrasound Parts:Save thousands on parts and machines. Up to 75% off OEM prices. (Site not responding. Last check: )
		diasonics part nimbers ► Ultrasound Parts:Save thousands on parts and machines.
		diasonics part nimbers helps people go undetected even though they are in plain sight.
		You hear about it any time it reaches a new high or a new low, and you also hear about it daily in statements.
	www.general-elecctric.he-ultrasound.com /diasonicspartnimbers.html (261 words)

	Algorithm (Site not responding. Last check: )
		The calculator adopts a brute force approach, i.e., it essentially computes the nimber of each of the followers and calculates the nim-sum of these nimbers.
		More precisely, the algorithm is as follows: a game with no string has nimber 0; given a position, the calculator first decides if there is any coin which is capturable.
		These pieces can be solved independently, and the nimber of the whole game will just be the nim-sum of these little pieces.
	www.eecs.berkeley.edu /~fmang/nimstring/algorithm.html (276 words)

	Doc/Articles/Play191 - J Wiki
		If the 'larger' of two different nimbers is 1 or 2 or 4 or 16 or 256 or 65536 or 4294967296 or ', you multiply them just as you multiply the corresponding ordinary numbers.
		The product of one of these special nimbers with itself is obtained by taking 1 1/2 times its ordinary value.
		I found it impossible to use this rule for nimbers greater than 4.
	www.jsoftware.com /jwiki/Doc/Articles/Play191 (2615 words)

	CHANCE News 10.04
		In their strategy session each player is assigned one of the seven non-zero nimbers and it is put on his hat for the others to see.
		But this cannot happen since it would mean that the sum of all nimbers of those with red hats is 000 and we have assumed this is not the case.
		Then the sum of the nimbers on the red hats he sees is 010 so the only case in which he would guess would be if he has the number 010.
	dartmouth.edu /~chance/chance_news/recent_news/chance_news_10.04.html (9212 words)

	Freddy Mang (Site not responding. Last check: )
		There were some bug fixes, and it should now print all the 1-step followers.
		According to the theory of Spargue and Grundy, every impartial game position can be reduced to a equivalent nim-heap.
		This nimstring calculator computes the nim-value, or nimber (size of nim-heap).
	www-cad.eecs.berkeley.edu /~fmang/nimstring (359 words)

	Combinatorial Amazons Databases (Site not responding. Last check: )
		My databases report that there are more amazons positions with a value of *2.
		Values like 2 are called nimbers* and appear in impartial games (where both players have exactly the same moves available from each position).
		Amazons is a partizan game (players may have different moves), and it is unusual for nimbers other than * to appear in such games.
	www.cs.ualberta.ca /~tegos/research/amazons/cd (136 words)

	California lotto plus winning nimbers (Site not responding. Last check: )
		With billions of sites on the internet, it is hard to find the report about california lotto plus winning nimbers that you need.
		So, whether you are interested in seeking advice for california lotto plus winning nimbers or tips on iowa power ball winning numbers, we provide a way to seek the correct instructions that is relevant to you.
		In just a few short years, the net has become the finest source of news.
	www.tskt.org /california-lotto-plus-winning-nimbers.html (651 words)

	HIV and AIDS
		According to the Filipino AIDS Task force and the National Center for Disease Control' HIV/AIDS Surveillance Report, Pilipinos have the highest rate of AIDS case in California.
		Of the 1919 API AIDS cases in California, Pilipinos comprise 33.1% of those nimbers, the biggest Asian Pacific Islander group.
		Since the beginning of the AIDS epidemic, Filipinos living in the U.S. have constituted the largest number of reported AIDS cases among all Asians and Pacific Islanders (APIs).
	members.tripod.com /~ucla_PCH/hivaids.htm (399 words)

	Sprague–Grundy theorem - Wikipedia, the free encyclopedia
		For the purposes of the Sprague–Grundy theorem, a game is a two-player game of perfect information satisfying the ending condition (all games come to an end: there are no infinite lines of play) and the normal play condition (a player who cannot move loses).
		We prove the theorem by structural induction on the set representing the game.
		By the induction hypothesis, all of the options are equivalent to nimbers, say G
	en.wikipedia.org /wiki/Sprague-Grundy_theorem (619 words)

	Scientific Commons: Kayles and Nimbers, Array [Hans L. Bodlaender, Dieter Kratsch]
		Scientific Commons: Kayles and Nimbers, Array [Hans L. Bodlaender, Dieter Kratsch]
		Two players select alternatingly a vertex from a given graph G - a chosen vertex may not be adjacent or equal to an already chosen vertex.
		It is shown that the problem can be solved in O(n^3) time on cocomparability graphs and circular arc graphs, and in O(n 1 1/ log 3) = O(n^1.631) time on cographs.
	de.scientificcommons.org /396833 (129 words)

	The Dispatch - Serving the Lexington, NC - News (Site not responding. Last check: )
		The set of all surreal numbers with birthday smaller than some inaccessible cardinal form a field.
		The set of nimbers with birthday smaller than
		, the nimbers with birthday smaller than any infinite cardinal are all examples of fields.
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Field_(mathematics) (1127 words)

	Citebase - Higher Nimbers in pawn endgames on large chessboards
		Citebase - Higher Nimbers in pawn endgames on large chessboards
		Higher Nimbers in pawn endgames on large chessboards
		Authors: Elkies, Noam D. We answer a question posed in [Elkies 1996] (math.CO/9905198) by constructing a class of pawn endgames on m-by-n boards that show the Nimbers *k for large k.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0011253 (168 words)

	Home page of Lowell Abrams (Site not responding. Last check: )
		In this context, we will study such fundamental notions as axiomatic system, specialized notation, symbolic manipulation, proof, rigor, heuristic, refinement of ideas, and effective communication of technical ideas.
		An application of loop and quasigroup theory to a particular table related to nimbers and sequential compound of games.
		I am always on the look-out for new and interesting ideas in algebraic topology, homological algebra, and algebraic combinatorics.
	home.gwu.edu /~labrams (1340 words)

	Here and Now : The Cheney Effect - 2/9/2004
		For the first time in his presidency, favorability ratings for President Bush have dropped below 50 percent in recent polls.
		Vice President Dick Cheney's favorability nimbers are much worse, around 20 percent in recent polls.
		In what's expected to be a close election, could this wide gap jeopardize Cheney's place on the ticket?
	www.here-now.org /shows/2004/02/20040209_3.asp (166 words)

	Organizing Goods Transport Office (Site not responding. Last check: )
		They are 13 in nimbers, distributed in various govermentes.
		To register public trucks in a queur to carry out transporting of goods for both public and private sector within Syria and outside.
		For more information, Please contact one of the indication addresses in the following table:
	www.mot.gov.sy /en/l_item.htm (137 words)

	Special project: Nimbers
		C] discovered that there is a collection of objects derived from combinatorial games which forms a field, called here the field of nimbers.
		We shall construct the set of nimbers, giving some examples along the way, but we shall not prove that it is a field.
		Using the above notation, we may compactly describe this set up as
	web.usna.navy.mil /~wdj/book/node88.html (428 words)

	COMMENT
		: even i don't know the model no. but i wrote the serial no. a all nimbers founded in the modem any how please try to get me the drvier as soon as possible
		: : even i don't know the model no. but i wrote the serial no. a all nimbers founded in the modem any how please try to get me the drvier as soon as possible : : thanks alot : The Motorola 62412-51 is the same modem as a Puretek PT-3027 and GVC 1156iv/m2d.
		Use this sites driver search feature and those keywords to find drivers listed in our user uploads section.
	www.driverguide.com /boards/modems7/1154.html (261 words)

	standard (Site not responding. Last check: )
		I'm don't think this is true in amalgamation Nim.
		Thus, Conway's Nimbers might not be directly useful.
		I didn't see the game mentioned in the two Conway books I have access to.
	forumgeom.fau.edu /POLYA/Inventory/Inventory007.html (267 words)

	Tubal Reversal Message Board: 2ND SET OF NIMBERS IN!!!
		Tubal Reversal Message Board: 2ND SET OF NIMBERS IN!!!
		Tubal Reversal Message Board » After Tubal Reversal » 2ND SET OF NIMBERS IN!!!
		That is great news, keep us posted with your progress.
	www.tubal-reversal.net /cgi-bin/ultimatebb.cgi?ubb=get_topic;f=5;t=010859;p=0 (266 words)

	PPT :: View topic - Werewolf 4 Excess (Nov. 20-21) (Site not responding. Last check: )
		I just want to know- What were the nimbers we picked while signing up for?
		Last time we had to give a random word, it was used on the tablet but since we have none this time...?
		HoroHoro wrote: flatluigi wrote: I just want to know- What were the nimbers we picked while signing up for?
	www.pinkpt.com /forum/archive/o_t__t_9416__start_105__index.html (731 words)

	Star Wars: Message Boards: Do you invest? Please answer. (Site not responding. Last check: )
		(If you do not wish to give actual nimbers, percentages will be fine)
		Do you think that you will have enough money for retirement?How much do you think that you will need to retire comfotably?
		I recently re-mortgaged which brought my monthly outgoings down by £200
	forums.starwars.com /thread.jspa?threadID=166198 (1315 words)

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	alexus.freeplayarcade.com /e/index11.html (64 words)

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