@prefix owl: . owl:sameAs . @prefix foaf: . foaf:page . @prefix rdfs: . rdfs:label "Conjunto universo"@pt , "Uniwersum (matematyka)"@pl , "Universe (mathematics)"@en , "Universum (Mathematik)"@de , "\u5168\u96C6"@zh , "Univerz\u00E1lis oszt\u00E1ly"@hu , "Univerz\u00E1ln\u00ED mno\u017Eina"@cs , "Universum (m\u00E4ngdteori)"@sv , "Conjunto universal"@es , "\u5168\u96C6"@ja . @prefix dbpprop: . dbpprop:abstract "Der Begriff Universum steht in der Mathematik z. B. f\u00FCr das so genannte Mengenuniversum U. Es fasst beliebige bekannte und unbekannte, \u00FCber Axiome definierte Objekte zusammen, auch Mengen von Objekten. Ein Universum wird meist \u00FCber eine Variable mit einer Aussage assoziiert. Ein Mengensystem U aus Mengen und Urelementen besitzt folgende Eigenschaften: Mit einer Menge <math> A </math> geh\u00F6ren auch alle Elemente von <math> A </math> zu U, d.h. wenn <math> A \\in U </math>, so <math> A \\subseteq U </math> Mit Mengen oder Urelementen <math> A, B </math> geh\u00F6rt auch die Zweiermenge <math> \\left\\{ A,B \\right\\} </math> zu U Mit einer Menge <math> A </math> geh\u00F6rt auch die Potenzmenge <math> \\mathfrak{P} \\left(A \\right) </math> zu U F\u00FCr jede Mengenfamilie <math> \\left(A_i \\right)_{i\\in I} </math>, deren Indexbereich <math> I </math> und deren s\u00E4mtliche Glieder <math> A_i </math> zu U geh\u00F6ren, geh\u00F6rt auch die Vereinigung <math> \\cup_{i\\in I} A_i </math> zu U U enth\u00E4lt wenigstens eine unendliche Menge Die Existenz eines Universums l\u00E4sst sich nur mittels sehr starker Axiome der Mengenlehre beweisen, die n\u00E4mlich die Existenz von Mengen mit sehr gro\u00DFer M\u00E4chtigkeit sichern, da ein Universum, wenn es existiert, eine sehr gro\u00DFe M\u00E4chtigkeit besitzt. Vielfach wird die Existenz eines Universums, genauer: dass jede Menge Element eines Universums ist, als Axiom gefordert, als Universenaxiom. Derartige Universen werden vor allem in der allgemeinen Strukturtheorie gefordert."@de , "El universo de discurso, conjunto universal o referencial, que normalmente se denota por las letras <math> U, \\; V \\; \\acute o \\; E \\,</math>, es un conjunto cuyo objeto de estudio son los subconjuntos del mismo. Anteriormente se consideraba al conjunto universal como el conjunto de todas las cosas, sin embargo est\u00E1 demostrado que este conjunto no existe. Particularmente porque suponer la existencia de dicho conjunto conduce a la paradoja de Russell. Actualmente se debe dejar en claro sobre cu\u00E1l conjunto se est\u00E1 tratando. Por ejemplo, si estamos tratando conjuntos cuyos elementos son letras, el conjunto referencial ser\u00EDa el conjunto formado por todas las letras del alfabeto. El complemento del conjunto universo es el conjunto vac\u00EDo, es decir, aquel que est\u00E1 desprovisto de elementos."@es , "\u6570\u5B66\u4E0A\uFF0C\u7279\u522B\u662F\u5728\u96C6\u5408\u8BBA\u548C\u6570\u5B66\u57FA\u7840\u7684\u5E94\u7528\u4E2D\uFF0C\u5168\u7C7B\uFF08\u82E5\u662F\u96C6\u5408\uFF0C\u5219\u4E3A\u5168\u96C6\uFF09\u5927\u7EA6\u662F\u8FD9\u6837\u4E00\u4E2A\u7C7B\uFF0C\u5B83\uFF08\u5728\u67D0\u79CD\u7A0B\u5EA6\u4E0A\uFF09\u5305\u542B\u4E86\u6240\u6709\u7684\u7814\u7A76\u5BF9\u8C61\u548C\u96C6\u5408\u3002"@zh , "Univerz\u00E1lis oszt\u00E1lynak nevezz\u00FCk a halmazelm\u00E9letben az \u00F6sszes halmaz oszt\u00E1ly\u00E1t. Alternat\u00EDv elnevez\u00E9sek: univerzum, halmazuniverzum. Bevett jel\u00F6l\u00E9se: <math>\\mathrm{V}</math>. Meghat\u00E1roz\u00E1sa: <math>\\mathrm{V}=\\{ x|\\,x=x\\}</math> Szavakban: <math>\\mathrm{V}</math> azon individuumok oszt\u00E1lya, amelyek azonosak \u00F6nmagukkal. Mivel az <math>x=x</math> formula logikai igazs\u00E1g, minden individuum eleme a <math>\\mathrm{V}</math> oszt\u00E1lynak. A legt\u00F6bb halmazelm\u00E9leti axi\u00F3marendszerben <math>\\mathrm{V}</math> val\u00F3di oszt\u00E1ly. Az ellenkez\u0151 feltev\u00E9s a Cantor-paradoxon n\u00E9ven ismert ellentmond\u00E1sra vezetne. Kiv\u00E9telt k\u00E9pez a New Foundations elm\u00E9letcsal\u00E1d, amelyben az univerz\u00E1lis oszt\u00E1ly halmaz, \u00E9s eleme \u00F6nmag\u00E1nak. A j\u00F3lfund\u00E1lt halmazelm\u00E9letekben <math>\\mathrm{V}</math> egybeesik a Russell-oszt\u00E1llyal. Ezekben az elm\u00E9letekben a Russell-paradoxon is akad\u00E1lyozza, hogy a halmazok k\u00F6z\u00E9 soroljuk. Atomos halmazelm\u00E9letekben a fenti meghat\u00E1roz\u00E1s az \u00F6sszes individuum oszt\u00E1ly\u00E1t vezeti be. Ha <math>\\mathrm{V}</math>-t nem az \u00F6sszes individuum, hanem az \u00F6sszes halmaz oszt\u00E1lyak\u00E9nt szeretn\u00E9nk meghat\u00E1rozni, akkor az al\u00E1bbi meghat\u00E1roz\u00E1ssal kell \u00E9ln\u00FCnk: <math>\\mathrm{V}=\\{ x|\\,\\mathrm{m}(x)\\}</math> (Itt <math>\\mathrm{m}</math> r\u00F6vid\u00EDti azt, hogy x halmaz.)"@hu , "Uniwersum \u2013 poj\u0119cie w matematyce oznaczaj\u0105ce klas\u0119 wszystkich element\u00F3w danego modelu matematycznego."@pl , "Universum \u00E4r ett begrepp \u00E4ven inom m\u00E4ngdteori. I naiv m\u00E4ngdl\u00E4ra avser universum vanligen den dom\u00E4n f\u00F6r tillf\u00E4llet beaktar till vilken de m\u00E4ngder som studeras \u00E4r delm\u00E4ngder och betecknas ibland med bokstaven U. G\u00E5r \u00E4ven under namnet grundm\u00E4ngd och betecknas d\u00E5 G. Komplementoperationen p\u00E5 en m\u00E4ngd f\u00F6ruts\u00E4tter att ett universum har specificerats. I axiomatisk m\u00E4ngdl\u00E4ra anv\u00E4nds begreppet universum ibland som synonym till begreppet modell f\u00F6r m\u00E4ngdl\u00E4ran."@sv , "\u5168\u96C6\uFF08\u305C\u3093\u3057\u3085\u3046\uFF09\u3068\u3044\u3046\u8A00\u8449\u306F\u3001\u4E3B\u306B\u7279\u5B9A\u306E\u4EBA\u7269\u306E\u5168\u8457\u4F5C\u3001\u5168\u6587\u7AE0\u3092\u53CE\u9332\u3057\u305F\u3082\u306E\u3001\u307E\u305F\u306F\u4E3B\u306A\u8457\u4F5C\u7B49\u3092\u9078\u3073\u7DE8\u96C6\u3057\u305F\u3082\u306E\u3001\u307E\u305F\u7279\u5B9A\u306E\u6642\u4EE3\u30FB\u56FD\u3084\u5730\u57DF\u306E\u4E3B\u8981\u306A\u6587\u5B66\u7684\u8457\u4F5C\u3092\u7DE8\u7E82\u3057\u305F\u3082\u306E\u3001\u548C\u6D0B\u306E\u7F8E\u8853\u30FB\u6B74\u53F2\u7684\u6587\u5316\u8CA1\u3092\u64AE\u5F71\u3057\u305F\u5199\u771F\u3092\u307E\u3068\u3081\u305F\u3082\u306E\uFF08\u65E5\u672C\u53E4\u5178\u6587\u5B66\u5168\u96C6\u3001\u4E16\u754C\u7F8E\u8853\u5168\u96C6\u306A\u3069\uFF09\u306A\u3069\u306B\u4F7F\u308F\u308C\u308B\u3002 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\u307E\u305F\u3001\u5927\u6B63\u6642\u4EE3\u4EE5\u964D\u76DB\u3093\u306B\u51FA\u7248\u3055\u308C\u305F\u3082\u306E\u3067\u3001\u300C\u4E16\u754C\u6587\u5B66\u5168\u96C6\u300D\u300C\u65E5\u672C\u6587\u5B66\u5168\u96C6\u300D\u306A\u3069\u3068\u79F0\u3059\u308B\u3082\u306E\u304C\u3042\u308B\u3002\u3053\u308C\u3089\u306F\u4EE3\u8868\u7684\u306A\u5C0F\u8AAC\u5BB6\u306E\u4E3B\u8981\u4F5C\u3092\u53CE\u3081\u308B\u3082\u306E\u3067\u3042\u308B\u304C\u3001\u30DA\u30FC\u30B8\u914D\u5206\u304C\u3042\u308B\u305F\u3081\u3001\u8AAD\u307F\u305F\u3044\u4F5C\u54C1\u304C\u63B2\u8F09\u3055\u308C\u3066\u3044\u308B\u3068\u306F\u9650\u3089\u306A\u3044\u3002\u5FDC\u63A5\u9593\u306E\u98FE\u308A\u306B\u306A\u3063\u3066\u3044\u308B\u3082\u306E\u3082\u591A\u3044\u3002\u3053\u308C\u3089\u306F\u5168\u96C6\u3068\u3044\u3046\u3088\u308A\u53E2\u66F8\u3068\u3044\u3046\u3079\u304D\u3067\u3042\u308B\u3002\u305F\u3060\u3057\u3001\u3053\u3046\u3057\u305F\u8AA4\u89E3\u3092\u3075\u305B\u3050\u305F\u3081\u304B\u3001\u300C\u5927\u7CFB\u300D\u3068\u540D\u4E57\u308B\u3082\u306E\u3082\u591A\u3044\u3002 \u3068\u3053\u308D\u3067\u3001\u6709\u9650\u306A\u300C\u5168\u96C6\u300D\u306B\u8AB0\u306E\u4F55\u3092\u5165\u308C\u3001\u5E7E\u5DFB\u3092\u3055\u304F\u304B\u3001\u8AB0\u3001\u4F55\u3092\u3044\u308C\u306A\u3044\u304B\u3068\u3044\u3046\u9078\u629E\u306F\u3001\u3059\u3050\u308C\u3066\u7DE8\u96C6\u7684\u884C\u70BA\u3067\u3042\u308A\u3001\u3053\u306E\u3046\u3048\u306A\u304F\u5177\u4F53\u7684\u306A\u6279\u8A55\u3067\u3082\u3042\u308A\u5F97\u308B\uFF08\u305F\u3068\u3048\u3070\u300E\u6587\u5B66\u5168\u96C6\u3092\u7ACB\u3061\u3042\u3052\u308B\u300F\u3000\u4E38\u8C37\u624D\u4E00\u3001\u4E09\u6D66\u96C5\u58EB\u3001\u9E7F\u5CF6\u8302\u30002006\u3000\u6587\u85DD\u6625\u79CB\u3002\u307E\u305F\u3001\u576A\u5185\u7950\u4E09\u306F\u3001\u307F\u305A\u304B\u3089\u304C\u7DE8\u96C6\u3057\u305F\u7B51\u6469\u66F8\u623F\u306E\u300C\u660E\u6CBB\u306E\u6587\u5B66\u300D\u306E\u30B7\u30EA\u30FC\u30BA\u306B\u3001\u9957\u5EAD\u7BC1\u6751\u306B1\u5DFB\u3092\u5272\u3044\u305F\u3053\u3068\u3092\u7279\u5FB4\u3068\u3057\u3066\u3044\u305F\u3002\u307E\u305F\u3001\u305F\u3068\u3048\u3070\u6C60\u6FA4\u590F\u6A39\u500B\u4EBA\u7DE8\u96C6\u300E\u4E16\u754C\u6587\u5B66\u5168\u96C6\u300F\u516824\u5DFB\u30002007\uFF5E\u3000\u6CB3\u51FA\u66F8\u623F\u65B0\u793E\u306E\u7DE8\u96C6\u3076\u308A\u3082\u3053\u306E\u5B9F\u4F8B\u3068\u3044\u3048\u3088\u3046\uFF09 \u4E2D\u56FD\u6587\u5B66\u8005\u306E\u9AD8\u5CF6\u4FCA\u7537\u306F\u3001\u5927\u5B66\u3067\u8B1B\u7FA9\u3057\u305F\u969B\u306B\u300C\u660E\u6CBB\u6587\u5B66\u5168\u96C6\u306B\u306F\u9AD8\u5CF6\u5148\u751F\u306E\u8A00\u3063\u305F\u300E\u25CB\u25CB\u4F5C\u306E\u00D7\u00D7\u300F\u3068\u3044\u3046\u4F5C\u54C1\u306F\u5165\u3063\u3066\u3044\u306A\u3044\u3002\u3086\u3048\u306B\u305D\u3093\u306A\u4F5C\u54C1\u306F\u5B58\u5728\u3057\u306A\u3044\u3001\u5618\u3092\u8A00\u308F\u306A\u3044\u3067\u4E0B\u3055\u3044\u300D\u3068\uFF08\u300C\u5168\u96C6\u300D\u3068\u3044\u3046\u8A00\u8449\u3092\u5B57\u7FA9\u901A\u308A\u306B\u89E3\u91C8\u3057\u305F\uFF09\u5927\u5B66\u751F\u306B\u8A70\u3081\u5BC4\u3089\u308C\u305F\u3068\u3044\u3046\uFF08\u3042\u307E\u308A\u306B\u305D\u306E\u5B66\u751F\u304C\u611A\u304B\u3059\u304E\u3066\u4FE1\u3058\u304C\u305F\u3044\u307B\u3069\u306E\uFF09\u4F53\u9A13\u3092\u66F8\u304D\u6B8B\u3057\u3066\u3044\u308B\u3002"@ja , "In mathematical logic, the universe of a structure (or model) is its domain. In mathematics, and particularly in set theory and the foundations of mathematics, a universe is a class that contains all the entities one wishes to consider in a given situation. There are several versions of this general idea, described in the following sections."@en , "Univerz\u00E1ln\u00ED mno\u017Eina (t\u00E9\u017E univerzum) je mno\u017Eina v\u0161ech prvk\u016F, kter\u00E9 jsou relevantn\u00ED v r\u00E1mci dan\u00E9ho kontextu (dom\u00E9ny, probl\u00E9mu). Univerz\u00E1ln\u00ED mno\u017Eina b\u00FDv\u00E1 ozna\u010Dov\u00E1na jako <math>I</math>."@cs , "Em certos problemas da Teoria dos Conjuntos, \u00E9 preciso que se defina um conjunto que contenha todos os conjuntos considerados. Assim, todos os conjuntos trabalhados no problema seriam subconjuntos de um conjunto maior, que \u00E9 conhecido como Conjunto Universo, ou simplesmente Universo. Por exemplo: em um problema envolvendo conjuntos de n\u00FAmeros inteiros, o conjunto dos n\u00FAmeros inteiros <math>\\mathbb{Z}</math> \u00E9 o Conjunto Universo."@pt ; rdfs:comment "El universo de discurso, conjunto universal o referencial, que normalmente se denota por las letras <math> U, \\; V \\; \\acute o \\; E \\,</math>, es un conjunto cuyo objeto de estudio son los subconjuntos del mismo. Anteriormente se consideraba al conjunto universal como el conjunto de todas las cosas, sin embargo est\u00E1 demostrado que este conjunto no existe. Particularmente porque suponer la existencia de dicho conjunto conduce a la paradoja de Russell."@es , "Univerz\u00E1lis oszt\u00E1lynak nevezz\u00FCk a halmazelm\u00E9letben az \u00F6sszes halmaz oszt\u00E1ly\u00E1t. Alternat\u00EDv elnevez\u00E9sek: univerzum, halmazuniverzum. Bevett jel\u00F6l\u00E9se: <math>\\mathrm{V}</math>. Meghat\u00E1roz\u00E1sa: <math>\\mathrm{V}=\\{ x|\\,x=x\\}</math> Szavakban: <math>\\mathrm{V}</math> azon individuumok oszt\u00E1lya, amelyek azonosak \u00F6nmagukkal."@hu , "In mathematical logic, the universe of a structure (or model) is its domain. In mathematics, and particularly in set theory and the foundations of mathematics, a universe is a class that contains all the entities one wishes to consider in a given situation. There are several versions of this general idea, described in the following sections."@en , ""@ja , "Univerz\u00E1ln\u00ED mno\u017Eina (t\u00E9\u017E univerzum) je mno\u017Eina v\u0161ech prvk\u016F, kter\u00E9 jsou relevantn\u00ED v r\u00E1mci dan\u00E9ho kontextu (dom\u00E9ny, probl\u00E9mu). Univerz\u00E1ln\u00ED mno\u017Eina b\u00FDv\u00E1 ozna\u010Dov\u00E1na jako <math>I</math>."@cs , "Uniwersum \u2013 poj\u0119cie w matematyce oznaczaj\u0105ce klas\u0119 wszystkich element\u00F3w danego modelu matematycznego."@pl , "Universum \u00E4r ett begrepp \u00E4ven inom m\u00E4ngdteori. I naiv m\u00E4ngdl\u00E4ra avser universum vanligen den dom\u00E4n f\u00F6r tillf\u00E4llet beaktar till vilken de m\u00E4ngder som studeras \u00E4r delm\u00E4ngder och betecknas ibland med bokstaven U. G\u00E5r \u00E4ven under namnet grundm\u00E4ngd och betecknas d\u00E5 G. Komplementoperationen p\u00E5 en m\u00E4ngd f\u00F6ruts\u00E4tter att ett universum har specificerats. I axiomatisk m\u00E4ngdl\u00E4ra anv\u00E4nds begreppet universum ibland som synonym till begreppet modell f\u00F6r m\u00E4ngdl\u00E4ran."@sv , "\u6570\u5B66\u4E0A\uFF0C\u7279\u522B\u662F\u5728\u96C6\u5408\u8BBA\u548C\u6570\u5B66\u57FA\u7840\u7684\u5E94\u7528\u4E2D\uFF0C\u5168\u7C7B\uFF08\u82E5\u662F\u96C6\u5408\uFF0C\u5219\u4E3A\u5168\u96C6\uFF09\u5927\u7EA6\u662F\u8FD9\u6837\u4E00\u4E2A\u7C7B\uFF0C\u5B83\uFF08\u5728\u67D0\u79CD\u7A0B\u5EA6\u4E0A\uFF09\u5305\u542B\u4E86\u6240\u6709\u7684\u7814\u7A76\u5BF9\u8C61\u548C\u96C6\u5408\u3002"@zh , "Em certos problemas da Teoria dos Conjuntos, \u00E9 preciso que se defina um conjunto que contenha todos os conjuntos considerados. Assim, todos os conjuntos trabalhados no problema seriam subconjuntos de um conjunto maior, que \u00E9 conhecido como Conjunto Universo, ou simplesmente Universo. Por exemplo: em um problema envolvendo conjuntos de n\u00FAmeros inteiros, o conjunto dos n\u00FAmeros inteiros <math>\\mathbb{Z}</math> \u00E9 o Conjunto Universo."@pt , "Der Begriff Universum steht in der Mathematik z. B. f\u00FCr das so genannte Mengenuniversum U. Es fasst beliebige bekannte und unbekannte, \u00FCber Axiome definierte Objekte zusammen, auch Mengen von Objekten. Ein Universum wird meist \u00FCber eine Variable mit einer Aussage assoziiert. Ein Mengensystem U aus Mengen und Urelementen besitzt folgende Eigenschaften: Mit einer Menge <math> A </math> geh\u00F6ren auch alle Elemente von <math> A </math> zu U, d.h."@de . @prefix skos: . skos:subject . @prefix ns5: . skos:subject ns5:Mathematical_logic , ns5:Set_families . @prefix ns6: . dbpprop:wikiPageUsesTemplate ns6:expert-subject ; dbpprop:date "November 2008"@en ; dbpprop:hasPhotoCollection ; dbpprop:disambiguates . @prefix dbpedia: . dbpedia:U-small dbpprop:redirect . dbpprop:redirect , , , . dbpedia:Universe_set dbpprop:redirect . dbpprop:redirect .