
	Where results make sense

Topic: Surreal number

In the News (Tue 2 Dec 08)

Damian Green

Sumner Redstone

Crimson Tide

Tommy Tuberville

Bill Clinton

Wayne Rooney

Vilasrao Deshmukh

Wake Forest

Grand Slam

Oklahoma State

	Surreal number - Wikipedia, the free encyclopedia
		In mathematics, the surreal numbers are a field containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number, and therefore the surreals are algebraically similar to superreal numbers and hyperreal numbers.
		The definition and construction of the surreals is due to John Conway, and exemplifies Conway's characteristic notational cleverness and originality.
		The surreal numbers were originally motivated by studies of the game Go, and there are numerous connections between popular games and the surreals.
	en.wikipedia.org /wiki/Surreal_number (3179 words)

	Number article - Number quantity whole numbers natural numbers counting negative integers - What-Means.com (Site not responding. Last check: 2007-07-20)
		The most familiar numbers are the whole numbers {0, 1, 2,...} denoted by W and the natural numbers {1, 2, 3,...} used for counting and denoted by N.
		Newer developments are the hyperreal numbers and the surreal numbers, which extend the real numbers by adding infinitesimal and infinitely large numbers.
		The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra; one obtains the groups, rings and fields.
	www.what-means.com /encyclopedia/Number (447 words)

	Kids.net.au - Encyclopedia Surreal number -
		The surreal numbers are a class of numbers which includes all of the real numbers, and additional "infinite" numbers which are larger than any real number.
		In this, the surreals are similar to the hyperreal numbers, but their construction is very different and the class of surreals is larger and contains the hyperreals as a subset.
		Surreal numbers were first proposed by John Conway and later detailed by Donald Knuth in his 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness.
	www.kids.net.au /encyclopedia-wiki/su/Surreal_number (2876 words)

	PlanetMath: surreal number
		Each surreal number consists of two parts (called the left and right), each of which is a set of surreal numbers.
		The surreal numbers satisfy the axioms for a field under addition and multiplication (whether they really are a field is complicated by the fact that they are too large to be a set).
		This is version 6 of surreal number, born on 2002-08-24, modified 2005-03-03.
	planetmath.org /encyclopedia/SurrealNumber.html (310 words)

	Ivars Peterson's MathLand
		Even among mathematicians, the study of surreal numbers is an obscure pastime.
		In the surreal number system, it's possible to talk about whether omega is odd or even, to add 1 to infinity, to divide infinity in half, to take its square root or logarithm, and so on.
		"Conway's Surreal Numbers" in Penrose Tiles to Trapdoor Ciphers.
	www.maa.org /mathland/mathland_3_18.html (1176 words)

	Sensei's Library: Surreal Numbers
		Surreal numbers are a generalization of numbers introduced by John Horton Conway in his book On Numbers and Games.
		A surreal number is a game in which all games in L and R are also surreal numbers, and in which every member of L is less than every member of R. I've cleaned up the relationship between numbers and games a bit, but without the definition of comparison it's still inadequate.
		In the game-theoretical interpretation of surreal numbers as (positions of) games, L is the list of options of the "left" player and R is the list of options of the "right" player.
	senseis.xmp.net /?SurrealNumbers (642 words)

	What's a number?
		Given the difficulty of establishing whether a given number is algebraic or not, this was one of Cantor's early surprising results.
		The rest of the complex numbers could also be defined by adding this new number i to the set of reals and postulating that usual arithmetic operations (addition, subtraction, multiplication) apply to the expanded set and all the laws known to hold for these operations hold for the new set as well.
		The rest of surreal numbers (included are the numbers we discussed so far and myriads of numbers some of which I have a difficulty imagining.) are formed starting with 0 and applying just two simple rules.
	www.cut-the-knot.org /do_you_know/numbers.shtml (3486 words)

	Bret Willet's paper on infinity
		Cardinal numbers are those which measure the number of objects in a set, as opposed to ordinal numbers, which are numbers with a fixed predecessor and successor.
		Surreal numbers are more useful than ordinal numbers in that we can conduct calculations with surreal numbers, but our usual rules of arithmetic do not apply to the surreal numbers.
		Surreal numbers that cannot be "broken down" any further are called travagances, of which there are two types, the extravagances and the intravagances.
	www.facstaff.bucknell.edu /udaepp/090/w3/bretw.htm (2365 words)

	Fuzzy game - Wikipedia, the free encyclopedia
		Left could move to 1, which is a win for Left, while Right could move to -1, which is a win for Right; again this is a first-player win.
		No fuzzy game can be a surreal number (as explained in the surreal number article).
		surreal number the introduction to "Constructing Surreal Numbers" then section 5.
	en.wikipedia.org /wiki/Fuzzy_game (282 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-07-20)
		An extravagance is a positive number that can't be arrived at by performing finitely many algebraic, logarithmic, or exponential operations on earlier numbers.
		Numbers whose decimal expansions terminate are rational numbers, and numbers whose decimal expansions are nonterminating are sometimes rational (1/3 =.333...) and sometimes irrational.
		When you are adding zeros to the end of a number like x=1.2736 it is like adding on 0/10^n, where the 0 is in the nth place to the right of the decimal.
	mathforum.org /library/drmath/view/53891.html (1052 words)

	[No title] (Site not responding. Last check: 2007-07-20)
		Surreal numbers are something of an extension to the theory of real numbers, relating somehow to Leibniz's theories of infintesimals.
		Surreal numbers were invented by John Conway, and include all natural numbers, negative numbers, fractions, irrational numbers, numbers bigger than infinity, and smaller than the smallest fraction.
		The first and simplest surreal number is zero, and is defined as having empty left and right sets: $X_L = X_R = \{\}$.
	www.cs.cmu.edu /~cache/knowledge/surreal_numbers.html (136 words)

	number - Wiktionary
		To label (items) with numbers; to assign numbers to (items).
		Number the baskets so that we can find them easily.
		I don't know how many books are in the library, but they must number in the thousands.
	en.wiktionary.org /wiki/Number (198 words)

	Learn more about Surreal number in the online encyclopedia.
		The surreal numbers are a class of numbers which includes all of the real numbers, and additional "infinite" numbers which are larger or smaller than any real number.
		This book is actually a mathematical novelette, and is notable as one of the rare cases where a new mathematical idea has been first presented in a work of fiction.
		For infinite left or right set, this is valid in an altered form, since infinite sets may not contain a maximal element.
	www.onlineencyclopedia.org /s/su/surreal_number.html (3155 words)

	Amazon.com: Books: The Number Devil : A Mathematical Adventure (Site not responding. Last check: 2007-07-20)
		In Number Hell/Number Heaven, Robert and the Devil meet famous mathematicians of the past and Robert is inducted into the ranks of number apprentices.
		Surreal touches (numbers flying in the air, floating in a swimming pool), fanciful names for mathematical terms (prima-donna numbers for prime numbers) and problems posed directly to the reader contribute to the playful tone.
		The Number Devil is about a young boy who has nightmares in his sleep every night until one night the number devil, who is a low-tempered mathematician, starts to tell him mathematical secrets and tricks for solving even the most compicated problems.
	www.amazon.com /exec/obidos/tg/detail/-/0805057706?v=glance (1888 words)

	[No title]
		As a last remark for those ignorant about what surreal numbers are, they are a Big extention of the real numbers, including infinities of several sizes (all ordinals and cardinals are there).
		Two functions assuming the same values at each and every surreal number must be considered DIFFERENT if the left and right options are not the same.
		E.g.: the function which is 0 for finite numbers, and omega for infinite numbers.
	www.ics.uci.edu /~eppstein/cgt/surreal.html (2202 words)

	[No title] (Site not responding. Last check: 2007-07-20)
		In many cases, the application of ``infinitely small'' numbers instead of ''small but finite'' numbers allows the use of the old numerical algorithm, but now with an error that in a rigorous way can be shown to become infinitely small (and hence irrelevant).
		The important properties of a program for the efficient generation of derivative code are the asymmetries between the number of inputs and outputs of program components at various levels of abstraction and the mathematical complexity of the involved operators.
		In practice, the decrease of the number of products does not lead to a decrease of run time, because current compilers do some sharing equivalent to a partial split and mismanage memory related to split variables.
	www.ii.uib.no /forskningsgrupper/opt/forskning/AD_bibs/ad1996.bib (3089 words)

	Amazon.com: Books: Surreal Numbers (Site not responding. Last check: 2007-07-20)
		Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created.
		Stanford mathematician D. Knuth, in his slim volume Surreal Numbers, attempts to impart to the reader the notion of surreal numbers by way of a very unusual tactic: the dialogue.
		It does little justice to the beauty of surreal numbers, and does even less in its explanation of their properties.
	www.amazon.com /exec/obidos/tg/detail/-/0201038129?v=glance (2329 words)

	[No title] (Site not responding. Last check: 2007-07-20)
		John Conway's surreal numbers form a fascinatingly rich system not yet widely appreciated, presented here in a much more accessible form than his original one.
		The nice functions are described "locally" by Taylor series at number arguments (like usual analytic functions) and by towers at "gaps" among the surreal numbers (a characteristically new concept).
		It follows, e g, that each "usual" nice function with domain extending to infinity is characterized by a specific surreal number (its value at the "simplest" infinite number, Cantor's omega), which behaves just like the function with respect to algebraic operations and relations.
	www.ma.hw.ac.uk /nbdes/kruskalabs.html (350 words)

	[No title]
		“Number Systems with Simplicity Hierarchies: A Generalization of Conway’s Theory of Surreal Numbers,” The Journal of Symbolic Logic 66 (2001), no.3, pp.
		Real Numbers, Generalizations of the Reals, and Theories of Continuua, edited with a General Introduction by Philip Ehrlich, Kluwer Academic Publishers, 1994.
		Real Numbers, Generalizations of the Reals, and Theories of Continua, edited with a General Introduction by Philip Ehrlich, Kluwer Academic Publishers, 1994.
	www.philosophy.ohiou.edu /ehrlich.html (970 words)

	Re: This week's summary
		Larry said that if someone wanted to hack > > surreal numbers into Perl 6.1 then that would be cool.
		The expression "surreal number" was coined by Knuth.
		For more info, the wikipedia is your friend: http://en.wikipedia.org/wiki/Surreal_number For the full story, read the book "Numbers and Games".
	www.mail-archive.com /perl6-language@perl.org/msg16637.html (163 words)

	[No title] (Site not responding. Last check: 2007-07-20)
		A few years ago John Horton Conway of the University of Cambridge hit on a remarkable new way to construct numbers...
		Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field.
		Every real number is surrounded by a host of new numbers that lie closer to it than any other ``real'' value does.
	infohost.nmt.edu /~jstarret/surreal.html (212 words)

	Knuth: Surreal Numbers
		The usual numbers are very familiar, but at root they have a very complicated structure.
		Surreals are in every logical, mathematical and aesthetic sense better.
		I am very grateful to Knuth for inventing this name [surreal numbers]---the original of ONAG said ``Because of the generality of this Class, we shall simply describe its members as numbers, without adding any restricting adjective.'' ``Surreal Numbers'' is much better!
	www-cs-faculty.stanford.edu /~knuth/sn.html (720 words)

	Another View of Nonstandard Analysis
		We identify the guests of R with certain of the numbers introduced by J. Conway [1976], and view all these numbers as points on a continuous number line.
		Harry Gonshor [1986] identified surreals with two-valued sequences, finite and infinite.
		Sequences of zeros and ones with *tag 1 are the characteristic sequences for the members of a nontrivial ultrafilter on the set of finite ordinals.
	www.haverford.edu /math/wdavidon/NonStd.html (1480 words)

	Publisher description for Library of Congress control number 86009668 (Site not responding. Last check: 2007-07-20)
		Publisher description for An introduction to the theory of surreal numbers / Harry Gonshor.
		The surreal numbers form a system which includes both the ordinary real numbers and the ordinals.
		Since their introduction by J. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties.
	www.loc.gov /catdir/description/cam031/86009668.html (142 words)

	real number - Wiktionary
		(mathematics) An element of the real numbers; real numbers include the rational numbers and the irrational numbers, but not the imaginary numbers or complex numbers
		Every integer is a real number, but not vice versa.
		Even if you pass sqrt an integer, it returns a real number.
	en.wiktionary.org /wiki/Real_number (64 words)

	[No title]
		\point N.~L. Alling [1989], Fundamentals of analysis over surreal number fields, {\em Rocky Mountain J. Math.\/} {\bf 19}, 565--573.
		\point P.~Erd\H{o}s, W.~R. Hare, S.~T. Hedetniemi and R.~C. Laskar [1987], On the equality of the Grundy and ochromatic numbers of a graph, {\em J. Graph Theory\/} {\bf 11}, 157--159.
		\point H.~Gonshor [1986], {\em An Introduction to the Theory of Surreal Numbers\/}, Cambridge University Press, Cambridge.
	www.wisdom.weizmann.ac.il /~fraenkel/Papers/gb.bbl (16831 words)

	Surreal number : Surreal numbers (Site not responding. Last check: 2007-07-20)
		Surreal number : Surreal numbers
		The class of surreal numbers forms a field, but the class of games doesn't.
		It uses material from the wikipedia article Surreal number : Surreal numbers.
	www.eurofreehost.com /su/Surreal_numbers_6.html (903 words)

Surreal number (Site not responding. Last check: 2007-07-20)

Surreal number

Surreal number
article at Free Euro Online Encyclopedia

It uses material from the wikipedia article Surreal number.

www.eurofreehost.com /su/Surreal_number_6.html (888 words)

Try your search on: Qwika (all wikis)

Topic: Surreal number

Ads by Google

Related Topics

In the News (Tue 2 Dec 08)