@prefix owl: . @prefix dbpedia: . dbpedia:Surreal_number owl:sameAs . @prefix foaf: . @prefix ns3: . dbpedia:Surreal_number foaf:page ns3:Surreal_number . @prefix dbpprop: . dbpedia:Surreal_number dbpprop:reference , , . @prefix rdfs: . dbpedia:Surreal_number rdfs:label "Surre\u00EBel getal"@nl , "Liczby nadrzeczywiste"@pl , "Surreaaliluku"@fi , "Surreale Zahl"@de , "Numero surreale"@it , "Surreella tal"@sv , "Nombre surr\u00E9el et pseudo-r\u00E9el"@fr , "\u8D85\u73FE\u5BE6\u6578"@zh , "N\u00FAmero surreal"@pt , "Surreal number"@en , "Nadre\u00E1ln\u00E9 \u010D\u00EDslo"@cs ; dbpprop:abstract "Liczby nadrzeczywiste s\u0105 klas\u0105 obiekt\u00F3w, spe\u0142niaj\u0105c\u0105 aksjomaty cia\u0142a, kt\u00F3ra zawiera w sobie zar\u00F3wno liczby rzeczywiste, hiperrzeczywiste, jak i porz\u0105dkowe. Tak jak liczby hiperrzeczywiste klasa ta zawiera r\u00F3wnie\u017C wielko\u015Bci niesko\u0144czone oraz niesko\u0144czenie ma\u0142e (infinitezymalne). Klasa liczb nadrzeczywistych oryginalnie zosta\u0142a oznaczona No, jednak ze wzgl\u0119du na podobie\u0144stwo do oznaczenia liczb naturalnych z zerem <math>\\mathbb{N}_0</math> poni\u017Cej u\u017Cyty zosta\u0142 symbol <math>F</math>."@pl , "In matematica i numeri surreali costituiscono un campo che contiene i numeri reali e anche numeri infiniti e infinitesimi, rispettivamente maggiori o minori in valore assoluto di qualunque numero reale positivo. Per questo motivo i numeri surreali sono algebricamente simili ai numeri superreali e iperreali. La definizione e la costruzione dei surreali sono dovute a John Horton Conway, ed esemplificano la sua originalit\u00E0 e la sua inventiva. Furono introdotti da Donald Knuth in un libro del 1974 dal titolo Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness . Questo libro \u00E8 un breve racconto matematico, e va notato che \u00E8 uno dei rari casi in cui una nuova idea matematica viene prima presentata in un lavoro di fantasia. Nel suo libro, che ha la forma di dialogo, Knuth ha coniato il termine numero surreale per quegli oggetti che Conway, in origine, aveva semplicemente chiamato numeri. A Conway piacque il nuovo nome tanto che, in seguito, lo adott\u00F2. Conway ha descritto i numeri surreali e li ha usati per analizzare i giochi nel suo libro del 1976 dal titolo On Numbers and Games."@it , "Surreaaliluku on matematiikassa luku, joka voi olla itseisarvoltaan my\u00F6s pienempi tai suurempi kuin mik\u00E4\u00E4n positiivinen reaaliluku. Surreaalilukujen kunta sis\u00E4lt\u00E4\u00E4 reaalilukujen lis\u00E4ksi sek\u00E4 \u00E4\u00E4rett\u00F6m\u00E4n suuret ett\u00E4 \u00E4\u00E4rett\u00F6m\u00E4n pienet luvut."@fi , "Die surrealen Zahlen bilden eine Klasse von Zahlen, die alle reellen Zahlen umfasst, sowie \u201Eunendlich gro\u00DFe\u201C Zahlen, die gr\u00F6\u00DFer sind als jede reelle Zahl. Dabei ist jede reelle Zahl von surrealen Zahlen umgeben, die ihr n\u00E4her sind als jede andere reelle Zahl, insbesondere gibt es \u201Einfinitesimale\u201C Zahlen, die n\u00E4her bei Null liegen als jede positive reelle Zahl. Darin stimmen sie mit den hyperreellen Zahlen \u00FCberein, aber sie werden auf eine v\u00F6llig andere Weise konstruiert und enthalten die hyperreellen Zahlen als Teilmenge. Das Wort \u201Esurreal\u201C entstammt dem franz\u00F6sischen und bedeutet \u201E\u00FCber der Wirklichkeit\u201C. Es wird auch f\u00FCr die Stilrichtung des Surrealismus verwendet. Surreale Zahlen wurden zuerst von John Conway vorgestellt und 1974 im Detail beschrieben in Donald E. Knuths Buch Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. Dieses Buch ist eigentlich kein Fachbuch, sondern eine Novelle, und es ist einer der wenigen F\u00E4lle, in denen eine neue mathematische Idee zuerst in einem literarischen Werk pr\u00E4sentiert wurde. In seinem Buch, das in Dialogform gehalten ist, pr\u00E4gte Knuth den Begriff surreale Zahlen f\u00FCr das, was Conway urspr\u00FCnglich nur Zahlen nannte. Conway gefiel der neue Name, sodass er ihn sp\u00E4ter \u00FCbernahm. Er beschrieb die surrealen Zahlen und nutzte sie zur Analyse von Spielen in seinem Buch On Numbers and Games (1976)."@de , "Nadre\u00E1ln\u00E9 \u010D\u00EDslo je spole\u010Dn\u00FDm z\u00FApln\u011Bn\u00EDm pojmu re\u00E1ln\u00E9ho, ordin\u00E1ln\u00EDho a hyperre\u00E1ln\u00E9ho \u010D\u00EDsla. Z \u010Dist\u011B matematick\u00E9ho hlediska je ka\u017Ed\u00E9 nadre\u00E1ln\u00E9 \u010D\u00EDslo uspo\u0159\u00E1dan\u00E1 dvojice mno\u017Ein nadre\u00E1ln\u00FDch \u010D\u00EDsel, kter\u00E1 nadto spl\u0148uje jist\u00E9 podm\u00EDnky."@cs , "\u5728\u6578\u5B78\u4E0A\uFF0C\u8D85\u73FE\u5BE6\u6578\u7CFB\u7D71\u662F\u4E00\u7A2E\u9023\u7E8C\u7D71\uFF0C\u5176\u4E2D\u542B\u6709\u5BE6\u6578\u4EE5\u53CA\u7121\u7AAE\u91CF\uFF0C\u5373\u7121\u7AAE\u5927\uFF08\u5C0F\uFF09\u91CF\uFF0C\u5176\u7D55\u5C0D\u503C\u5927\uFF08\u5C0F\uFF09\u65BC\u4EFB\u4F55\u6B63\u5BE6\u6578\u3002\u8D85\u73FE\u5BE6\u6578\u8207\u5BE6\u6578\u6709\u8A31\u591A\u5171\u540C\u6027\u8CEA\uFF0C\u5305\u62EC\u5176\u5168\u5E8F\u95DC\u4FC2 \u300C\u2264\u300D \u4EE5\u53CA\u901A\u5E38\u7684\u7B97\u8853\u904B\u7B97\uFF08\u52A0\u6E1B\u4E58\u9664\uFF09\uFF1B\u4E5F\u56E0\u6B64\uFF0C\u5B83\u5011\u69CB\u6210\u4E86\u6709\u5E8F\u57DF\u3002\u5728\u56B4\u683C\u7684\u96C6\u5408\u8AD6\u610F\u7FA9\u4E0B\uFF0C\u8D85\u73FE\u5BE6\u6578\u662F\u53EF\u80FD\u51FA\u73FE\u7684\u6709\u5E8F\u57DF\u4E2D\u6700\u5927\u7684\uFF1B\u5176\u4ED6\u7684\u6709\u5E8F\u57DF\uFF0C\u5982\u6709\u7406\u6578\u57DF\u3001\u5BE6\u6578\u57DF\u3001\u6709\u7406\u51FD\u6578\u57DF\u3001 \u5217\u7DAD-\u5947\u7DAD\u5854\u57DF\uFF08Levi-Civita field\uFF09\u3001\u4E0A\u8D85\u5BE6\u6578\u57DF\u548C\u8D85\u5BE6\u6578\u57DF\u7B49\uFF0C\u5168\u90FD\u662F\u8D85\u73FE\u5BE6\u6578\u57DF\u7684\u5B50\u57DF\u3002\u8D85\u73FE\u5BE6\u6578\u57DF\u4E5F\u5305\u542B\u53EF\u9054\u5230\u7684\u3001\u5728\u96C6\u5408\u8AD6\u88E1\u69CB\u9020\u904E\u7684\u6240\u6709\u8D85\u9650\u5E8F\u6578\u3002 \u8D85\u73FE\u5BE6\u6578\u662F\u7531\u7D04\u7FF0\u00B7\u4F55\u9813\u00B7\u5EB7\u5A01\uFF08John Horton Conway\uFF09\u6240\u5B9A\u7FA9\u548C\u69CB\u9020\u7684\u3002\u9019\u500B\u540D\u7A31\u65E9\u57281974\u5E74\u4FBF\u5DF2\u7531\u9AD8\u5FB7\u7D0D\uFF08Donald Knuth\uFF09\u5728\u4ED6\u7684\u66F8\u300A\u8D85\u73FE\u5BE6\u6578\u300B\u4E2D\u5C31\u88AB\u5F15\u9032\u4E86\u3002\u300A\u8D85\u73FE\u5BE6\u6578\u300B\u662F\u4E00\u90E8\u4E2D\u77ED\u7BC7\u6578\u5B78\u5C0F\u8AAA\uFF0C\u800C\u503C\u5F97\u4E00\u63D0\u7684\u662F\uFF0C\u9019\u7A2E\u628A\u65B0\u7684\u6578\u5B78\u6982\u5FF5\u5728\u4E00\u90E8\u5C0F\u8AAA\u4E2D\u63D0\u51FA\u4F86\u7684\u60C5\u5F62\u662F\u975E\u5E38\u5C11\u6709\u7684\u3002\u5728\u9019\u90E8\u7531\u5C0D\u8A71\u9AD4\u5BEB\u6210\u7684\u8457\u4F5C\u88E1\uFF0C\u5510\u7D0D\u5FB7\u9020\u4E86\u300Csurreal number\u300D\u4E00\u8A5E\uFF0C\u7528\u4F86\u6307\u7A31\u5EB7\u5A01\u8D77\u521D\u53EA\u53EB\u505A\u300Cnumber\u300D\uFF08\u6578\uFF09\u7684\u9019\u500B\u65B0\u6982\u5FF5\u3002\u5EB7\u5A01\u6A02\u65BC\u63A1\u7528\u65B0\u7684\u540D\u7A31\uFF0C\u5F8C\u4F86\u5728\u4ED61976\u5E74\u7684\u8457\u4F5C\u300A\u8AD6\u6578\u5B57\u8207\u535A\u5F08\u300B\uFF08On Numbers and Games\uFF09\u4E2D\u5C31\u63CF\u8FF0\u4E86\u8D85\u73FE\u5BE6\u6578\u7684\u6982\u5FF5\u4E26\u4F7F\u7528\u5B83\u4F86\u9032\u884C\u4E86\u4E00\u4E9B\u535A\u5F08\u5206\u6790\u3002"@zh , "De surre\u00EBle getallen vormen een uitbreiding van de re\u00EBle getallen. De verzameling van surre\u00EBle getallen wordt wel aangegeven met \u05D0o (alef-nul). Net als de re\u00EBle getallen vormen de surre\u00EBle getallen een totaal geordend veld (in Belgi\u00EB) / lichaam (in Nederland). In tegenstelling tot de re\u00EBle getallen bevat \u05D0o ook infinitesimalen (d.w.z. oneindig kleine) en oneindig grote elementen. In zekere zin vormen de surre\u00EBle getallen de grootst mogelijke van al dergelijke uitbreidingen. De surre\u00EBle getallen kunnen opgebouwd worden vanuit de lege verzameling, door toepassing van het principe van Dedekindsneden, dat ook ten grondslag ligt aan de re\u00EBle getallen. In een oneindige reeks tussenstappen worden voortdurend nieuwe getallen gedefinieerd in termen van eerder gedefinieerde. Surre\u00EBle getallen werden ontwikkeld door de Engelse wiskundige John Horton Conway als een nevenresultaat van onderzoek naar de structuur van een bepaalde klasse van wiskundige spellen. De naam werd echter bedacht door Donald Knuth, maar werd later ook door Conway gebruikt."@nl , "Em matem\u00E1tica, os n\u00FAmeros surreais s\u00E3o uma classe de n\u00FAmeros que inclui todos os n\u00FAmeros reais e tamb\u00E9m n\u00FAmeros \"infinitos\", maiores ou menores que qualquer n\u00FAmero real; tamb\u00E9m inclui n\u00FAmeros \"infinitesimais\", que est\u00E3o mais pr\u00F3ximos do zero que qualquer n\u00FAmero real. Todos os n\u00FAmeros reais est\u00E3o rodeados de n\u00FAmeros surreais, que est\u00E3o mais pr\u00F3ximos de si do que qualquer n\u00FAmero real. Os n\u00FAmeros surreais t\u00EAm estrutura de corpo ordenado, o que significa que as quatro opera\u00E7\u00F5es aritm\u00E9ticas b\u00E1sicas s\u00E3o definidas e se comportam como esperado. O inverso multiplicativo de um n\u00FAmero infinito \u00E9 um infinitesimal n\u00E3o-nulo, e vice-versa. Nisto, os surreais s\u00E3o semelhantes aos n\u00FAmeros hiperreais, mas a sua constru\u00E7\u00E3o \u00E9 muito diferente. A classe dos surreais \u00E9 maior e inclui os hiperreais como tamb\u00E9m os ordinais de Cantor como subclasses. Os matem\u00E1ticos elogiaram os surreais por serem mais simples, mais gerais e constru\u00EDdos de forma mais limpa do que o sistema, mais comum, dos n\u00FAmeros reais. Os n\u00FAmeros surreais foram inicialmente propostos por John H. Conway por volta de 1970, e mais tarde desenvolvidos por Donald Knuth no seu livro de 1974 Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. Este livro era, na realidade, uma noveleta matem\u00E1tica e \u00E9 not\u00E1vel por ser um dos raros casos em que uma nova id\u00E9ia matem\u00E1tica foi apresentada pela primeira vez numa obra de fic\u00E7\u00E3o. No seu livro, que toma a forma de di\u00E1logo, Knuth criou o termo n\u00FAmeros surreais para aquilo que Conway tinha simplesmente chamado n\u00FAmeros. Conway gostou do novo nome, e adoptou-o mais tarde ele mesmo. Conway ent\u00E3o descreveu os n\u00FAmeros surreais e usou-os para analisar jogos no seu livro de 1976 On Numbers and Games. No contexto da teoria dos conjuntos, n\u00E3o existe o conjuntos dos n\u00FAmeros surreais, que, se existisse, teria a cardinalidade do conjunto de todos os conjuntos."@pt , "En math\u00E9matiques, les nombres surr\u00E9els sont un corps qui inclut tous les nombres r\u00E9els, ainsi que tous les ordinaux transfinis et leurs inverses, respectivement plus grands et plus petits que n'importe quel nombre r\u00E9el positif. Les nombres surr\u00E9els ont \u00E9t\u00E9 introduits par John Conway et popularis\u00E9s par Donald Knuth en 1974 dans son livre Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness . Les nombres pseudo-r\u00E9els, \u00E9galement introduits par Knuth, sont un sur-ensemble des nombres surr\u00E9els, construit avec des conditions plus faibles que ces derniers."@fr , "Mellan heltalen ligger de reella talen. P\u00E5 samma s\u00E4tt finns mellan Cantors ordinaltal de surreella talen. De konstruerades av John Conway i b\u00F6rjan av 1970-talet. Termen surreella tal myntades f\u00F6rst av Donald Knuth, en kollega till Conway, i en novell 1973. Conway kopplar de surreella talen till spelet Hackenbush. Det visar sig n\u00E4mligen vid studier av detta spel att varje Hackenbushst\u00E4llning har ett v\u00E4rde, som \u00E4r ett surreellt tal, och att varje surreellt tal motsvaras av en Hackenbushst\u00E4llning."@sv , "In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order \u2264 and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered Field. In a rigorous set theoretic sense, the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals. The surreals also contain all transfinite ordinal numbers reachable in the set theory in which they are constructed. The definition and construction of the surreals is due to John Horton Conway. They were introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. This book is a mathematical novelette, and is notable as one of the rare cases where a new mathematical idea was first presented in a work of fiction. In his book, which takes the form of a dialogue, Knuth coined the term surreal numbers for what Conway had simply called numbers originally. Conway liked the new name, and later adopted it himself. Conway then described the surreal numbers and used them for analyzing games in his 1976 book On Numbers and Games. In fact this attribution, while widely believed, is not fully correct. The idea of surreals and the rigorous definition of infinitesimal numbers was known at least as early as 1901, as can be seen on page 29 of Poincar\u00E9\u2019s 1901 Science and Hypothesis. A recent, rigorous treatment is Badiou's 1990 Le Nombre et les nombres."@en ; rdfs:comment "Die surrealen Zahlen bilden eine Klasse von Zahlen, die alle reellen Zahlen umfasst, sowie \u201Eunendlich gro\u00DFe\u201C Zahlen, die gr\u00F6\u00DFer sind als jede reelle Zahl. Dabei ist jede reelle Zahl von surrealen Zahlen umgeben, die ihr n\u00E4her sind als jede andere reelle Zahl, insbesondere gibt es \u201Einfinitesimale\u201C Zahlen, die n\u00E4her bei Null liegen als jede positive reelle Zahl."@de , ""@zh , "Liczby nadrzeczywiste s\u0105 klas\u0105 obiekt\u00F3w, spe\u0142niaj\u0105c\u0105 aksjomaty cia\u0142a, kt\u00F3ra zawiera w sobie zar\u00F3wno liczby rzeczywiste, hiperrzeczywiste, jak i porz\u0105dkowe. Tak jak liczby hiperrzeczywiste klasa ta zawiera r\u00F3wnie\u017C wielko\u015Bci niesko\u0144czone oraz niesko\u0144czenie ma\u0142e (infinitezymalne)."@pl , "Em matem\u00E1tica, os n\u00FAmeros surreais s\u00E3o uma classe de n\u00FAmeros que inclui todos os n\u00FAmeros reais e tamb\u00E9m n\u00FAmeros \"infinitos\", maiores ou menores que qualquer n\u00FAmero real; tamb\u00E9m inclui n\u00FAmeros \"infinitesimais\", que est\u00E3o mais pr\u00F3ximos do zero que qualquer n\u00FAmero real. Todos os n\u00FAmeros reais est\u00E3o rodeados de n\u00FAmeros surreais, que est\u00E3o mais pr\u00F3ximos de si do que qualquer n\u00FAmero real."@pt , "Nadre\u00E1ln\u00E9 \u010D\u00EDslo je spole\u010Dn\u00FDm z\u00FApln\u011Bn\u00EDm pojmu re\u00E1ln\u00E9ho, ordin\u00E1ln\u00EDho a hyperre\u00E1ln\u00E9ho \u010D\u00EDsla. Z \u010Dist\u011B matematick\u00E9ho hlediska je ka\u017Ed\u00E9 nadre\u00E1ln\u00E9 \u010D\u00EDslo uspo\u0159\u00E1dan\u00E1 dvojice mno\u017Ein nadre\u00E1ln\u00FDch \u010D\u00EDsel, kter\u00E1 nadto spl\u0148uje jist\u00E9 podm\u00EDnky."@cs , "De surre\u00EBle getallen vormen een uitbreiding van de re\u00EBle getallen. De verzameling van surre\u00EBle getallen wordt wel aangegeven met \u05D0o (alef-nul). Net als de re\u00EBle getallen vormen de surre\u00EBle getallen een totaal geordend veld (in Belgi\u00EB) / lichaam (in Nederland). In tegenstelling tot de re\u00EBle getallen bevat \u05D0o ook infinitesimalen (d.w.z. oneindig kleine) en oneindig grote elementen. In zekere zin vormen de surre\u00EBle getallen de grootst mogelijke van al dergelijke uitbreidingen."@nl , "In matematica i numeri surreali costituiscono un campo che contiene i numeri reali e anche numeri infiniti e infinitesimi, rispettivamente maggiori o minori in valore assoluto di qualunque numero reale positivo. Per questo motivo i numeri surreali sono algebricamente simili ai numeri superreali e iperreali. La definizione e la costruzione dei surreali sono dovute a John Horton Conway, ed esemplificano la sua originalit\u00E0 e la sua inventiva."@it , "En math\u00E9matiques, les nombres surr\u00E9els sont un corps qui inclut tous les nombres r\u00E9els, ainsi que tous les ordinaux transfinis et leurs inverses, respectivement plus grands et plus petits que n'importe quel nombre r\u00E9el positif. Les nombres surr\u00E9els ont \u00E9t\u00E9 introduits par John Conway et popularis\u00E9s par Donald Knuth en 1974 dans son livre Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness ."@fr , "Surreaaliluku on matematiikassa luku, joka voi olla itseisarvoltaan my\u00F6s pienempi tai suurempi kuin mik\u00E4\u00E4n positiivinen reaaliluku. Surreaalilukujen kunta sis\u00E4lt\u00E4\u00E4 reaalilukujen lis\u00E4ksi sek\u00E4 \u00E4\u00E4rett\u00F6m\u00E4n suuret ett\u00E4 \u00E4\u00E4rett\u00F6m\u00E4n pienet luvut."@fi , "Mellan heltalen ligger de reella talen. P\u00E5 samma s\u00E4tt finns mellan Cantors ordinaltal de surreella talen. De konstruerades av John Conway i b\u00F6rjan av 1970-talet. Termen surreella tal myntades f\u00F6rst av Donald Knuth, en kollega till Conway, i en novell 1973. Conway kopplar de surreella talen till spelet Hackenbush."@sv , "In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order \u2264 and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered Field."@en . @prefix skos: . @prefix ns7: . dbpedia:Surreal_number skos:subject ns7:Infinity , ns7:Real_closed_field , ns7:Mathematical_logic , ns7:Combinatorial_game_theory . @prefix ns8: . dbpedia:Surreal_number dbpprop:wikiPageUsesTemplate ns8:planetmath_reference ; dbpprop:id 3352 ; dbpprop:title "Surreal number"@en . @prefix ns9: . dbpedia:Surreal_number dbpprop:relatedInstance ns9:portal1 , ns9:portal2 . @prefix ns10: . dbpedia:Surreal_number dbpprop:hasPhotoCollection ns10:Surreal_number . dbpedia:Surreal dbpprop:disambiguates dbpedia:Surreal_number . dbpedia:Surreal_Numbers dbpprop:redirect dbpedia:Surreal_number . dbpedia:Surreal_numbers dbpprop:redirect dbpedia:Surreal_number . dbpedia:Surreals dbpprop:redirect dbpedia:Surreal_number . dbpedia:Conway_number dbpprop:redirect dbpedia:Surreal_number . dbpedia:Conway_numbers dbpprop:redirect dbpedia:Surreal_number . dbpedia:SurrealNumbers dbpprop:redirect dbpedia:Surreal_number .