@prefix rdfs: . @prefix dbr: . dbr:Up_to rdfs:label "\u0422\u043E\u0447\u043D\u0456\u0441\u0442\u044C \u0434\u043E"@uk , "Up to"@zh , "\u9055\u3044\u3092\u9664\u3044\u3066"@ja , "Llevat de"@ca , "Up to"@en , "Salvo (matem\u00E1ticas)"@es , "A\u017E na"@cs , "\u00C0 quelque chose pr\u00E8s"@fr , "Salvo (matem\u00E1tica)"@pt ; rdfs:comment "En matem\u00E0tiques, el terme llevat de indica que l'objecte gramatical \u00E9s una classe d'equival\u00E8ncia, que hom ha de considerar com una entitat simple. Si aquest objecte \u00E9s una classe de transformacions (com per exemple \"isomorfisme\" o \"permutaci\u00F3\"), aix\u00F2 implica l'equival\u00E8ncia d'objectes, un dels quals \u00E9s la imatge de l'altre per aquesta transformaci\u00F3. En contextos informals, els matem\u00E0tics acostumen a emprar el terme m\u00F2dul (o simplement \"mod\") per prop\u00F2sits similars, com per exemple \"m\u00F2dul un isomorfisme\"."@ca , "En matem\u00E1ticas, el t\u00E9rmino salvo , o a menos de , describe la relaci\u00F3n en la que los miembros de alg\u00FAn conjunto pueden ser vistos como equivalentes para alg\u00FAn prop\u00F3sito. describe una propiedad o proceso que transforma un elemento en otro de la misma clase de equivalencia, es decir, uno que se considera equivalente a \u00E9l. N\u00F3tese que en este contexto, la expres\u00F3n \u00ABsalvo\u00BB no tiene un sentido de excepci\u00F3n o de exclusi\u00F3n, sino por el contrario, de inclusi\u00F3n o equivalencia."@es , "\u5728\u6570\u5B66\u9886\u57DF\uFF0C\u8A5E\u7D44\u201Cup to xxx\u201D\u8868\u793A\u4E3A\u4E86\u67D0\u79CD\u76EE\u7684\u540C\u4E00\u7B49\u4EF7\u7C7B\u4E2D\u7684\u5143\u7D20\u89C6\u4E3A\u4E00\u4F53\u3002\u201Cxxxx\u201D\u63CF\u8FF0\u4E86\u67D0\u79CD\u6027\u8D28\u6216\u5C06\u4E2D\u5143\u7D20\u53D8\u4E3A\u540C\u4E00\u7B49\u4EF7\u7C7B\u4E2D\u53E6\u4E00\u4E2A\u7684\u64CD\u4F5C\uFF08\u5373\u5C06\u5143\u7D20\u548C\u5B83\u53D8\u4E3A\u7684\u90A3\u4E2A\u7B49\u4EF7\uFF09\u3002\u4F8B\u5982\u5728\u7FA4\u8BBA\u4E2D\uFF0C\u6211\u4EEC\u6709\u4E00\u4E2A\u7FA4G\u4F5C\u7528\u5728\u96C6\u5408X\u4E0A\uFF0C\u5728\u6B64\u60C5\u5F62\uFF1A\u5982\u679CX\u4E2D\u4E24\u4E2A\u5143\u7D20\u5728\u540C\u4E00\u8F68\u9053\u4E2D\uFF0C\u6211\u4EEC\u53EF\u4EE5\u8BF4\u5B83\u4EEC\u7B49\u4EF7\u201Cup to\u7FA4\u4F5C\u7528\u201D\u3002 \u4E2D\u6587\u4E2D\u6CA1\u6709\u7C7B\u4F3C\u5BF9\u5E94\u7684\u8BCD\u7EC4\uFF0C\u7FFB\u8B6F\u6210\u4E2D\u6587\u6642\uFF0C\u53EF\u4EE5\u659F\u914C\u8B6F\u70BA\uFF1A\u300C\u4E0D\u5225\u22EF\u22EF\u4E4B\u7570\u300D\u3001\u300C\u4E0D\u8FA8\u22EF\u22EF\u4E4B\u5225\u300D\u3001\u201C\u5728xxx\u7684\u610F\u4E49\u4E0B\u201D\u3001\u201C\u5DEE\u4E00\u4E2Axxx\u201D\u7B49\u3002\u6BD4\u5982\u4E0A\u9762\u53EF\u4EE5\u7FFB\u8BD1\u4E3A\u201C\u5DEE\u4E00\u4E2A\u7FA4\u4F5C\u7528\u7684\u610F\u4E49\u4E0B\u7B49\u4EF7\u201D\u3002\u4F46\u662F\uFF0C\u9019\u500B\u7FFB\u8B6F\u662F\u65E2\u8FC2\u8FF4\u53C8\u7B28\u62D9\uFF0C\u56E0\u70BA\u6578\u5B78\u4E2D\u300C\u5728xxx\u7684\u610F\u7FA9\u4E0B\u300D\u901A\u5E38\u662F\u5C0D\u6709\u6578\u500B\u4E0D\u7B49\u50F9\u5B9A\u7FA9\u7684\u8A5E\u8A9E\u6307\u5B9A\u5176\u610F\u7FA9\uFF0C\u5C0D\u61C9\u82F1\u6587\u201Cin the sense of\u201D\uFF0C\u4F8B\u5982\u300C\u9019\u500B\u51FD\u6578\u5728\u52D2\u8C9D\u683C\u7684\u610F\u7FA9\u4E0B\u53EF\u7A4D\uFF0C\u4F46\u662F\u5728\u9ECE\u66FC\u7684\u610F\u7FA9\u4E0B\u4E0D\u53EF\u7A4D\u300D\uFF0C\u5C31\u5C0D\u300C\u53EF\u7A4D\u300D\u4E00\u8A5E\u5148\u5F8C\u6307\u5B9A\u5169\u500B\u4E0D\u7B49\u50F9\u7684\u5B9A\u7FA9\uFF1B\u7136\u800C\uFF0C\u6578\u5B78\u4E2D\u82F1\u6587\u77ED\u8A9E\u201Cup to\u201D\u7684\u91CD\u9EDE\u4E0D\u5728\u78BA\u5B9A\u67D0\u8A5E\u8A9E\u7684\u5B9A\u7FA9\uFF0C\u800C\u5728\u7701\u7565\u6389\u4E00\u4E9B\u975E\u672C\u8CEA\u7684\u6B21\u8981\u5DEE\u7570\u3002"@zh , "\u6570\u5B66\u306E\u6587\u8108\u306B\u304A\u3051\u308B\u300C\u2014\uFF08\u306E\u9055\u3044\uFF09\u3092\u9664\u3044\u3066\u2026\u300D (\u306E\u3061\u304C\u3044\u3092\u306E\u305E\u3044\u3066\u3001\u2026 \"up to\" \u2014) \u3068\u3044\u3046\u8A9E\u53E5\u306F\u3001\u300C\u2014 \u306B\u95A2\u3059\u308B\u5DEE\u7570\u3092\u7121\u8996\u3059\u308B\u300D\u3053\u3068\u3092\u610F\u5473\u3059\u308B\u5C02\u9580\u7528\u8A9E\u3067\u3042\u308B\u3002\u3053\u306E\u8A00\u3044\u56DE\u3057\u306E\u610F\u5473\u3059\u308B\u3068\u3053\u308D\u306F\u3001\u300C\u9069\u5F53\u306A\u76EE\u7684\u306E\u3082\u3068\u3067\u306F\u3001\u3042\u308B\u3072\u3068\u3064\u306E\u540C\u5024\u985E\u306B\u5C5E\u3059\u308B\u5143\u5168\u4F53\u3092\u3001\u4F55\u304B\u5358\u4E00\u306E\u5B9F\u4F53\u3092\u8868\u3059\u3082\u306E\u3068\u307F\u306A\u305B\u308B\u300D\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308B\u3002\"\u2014\" \u306E\u90E8\u5206\u306B\u306F\u3001\u4F55\u3089\u304B\u306E\u6027\u8CEA\u3084\u3001\u540C\u3058\u540C\u5024\u985E\u306B\u5C5E\u3059\u308B\u5143(\u3064\u307E\u308A\u4E00\u65B9\u306F\u4ED6\u65B9\u306B\u540C\u5024\u3068\u306A\u308B\u3088\u3046\u306A\u5143)\u306E\u9593\u306E\u5909\u63DB\u306E\u904E\u7A0B\u3092\u8A18\u8FF0\u3059\u308B\u5185\u5BB9\u304C\u5165\u308B\u3002 \u305F\u3068\u3048\u3070\u4E0D\u5B9A\u7A4D\u5206\u3092\u8A08\u7B97\u3059\u308B\u3068\u304D\u3001\u305D\u306E\u7D50\u679C\u306F\u300C\u5B9A\u6570\u9805\u306E\u9055\u3044\u3092\u9664\u3044\u3066\u300D f\u2009(x) \u3067\u3042\u308B\u3068\u3044\u3046\u3088\u3046\u306B\u8A00\u3046\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u305D\u306E\u610F\u5473\u306F\u3001f\u2009(x) \u4EE5\u5916\u306B\u4E0D\u5B9A\u7A4D\u5206 g(x) \u304C\u3042\u3063\u305F\u3068\u3057\u3066\u3082 g(x) = f\u2009(x) + C (C \u306F\u5B9A\u6570)\u3068\u66F8\u304F\u3053\u3068\u304C\u3067\u304D\u3001\u305D\u306E\u5F8C\u306E\u8AD6\u7406\u5C55\u958B\u306B\u304A\u3044\u3066 f \u306E\u304B\u308F\u308A\u306B g \u3092\u7528\u3044\u3066\u3082\u5F71\u97FF\u304C\u306A\u3044\u3053\u3068\u3092\u793A\u5506\u3057\u3066\u3044\u308B\u3002\u307E\u305F\u4F8B\u3048\u3070\u7FA4\u8AD6\u3067\u3001\u7FA4 G \u304C X \u306B\u4F5C\u7528\u3059\u308B\u3068\u304D\u3001X \u306E\u3075\u305F\u3064\u306E\u5143\u304C\u540C\u3058\u306B\u5C5E\u3059\u308B\u306A\u3089\u3070\u3001\u305D\u308C\u3089\u306F\u300C\u7FA4\u4F5C\u7528\u306E\u9055\u3044\u3092\u9664\u3044\u3066\u300D\u540C\u5024\u3067\u3042\u308B\u3068\u8A00\u3044\u8868\u3059\u3053\u3068\u304C\u3067\u304D\u308B\u3002"@ja , "En math\u00E9matiques, l'expression \u00AB \u00E0 quelque chose pr\u00E8s \u00BB peut avoir plusieurs sens diff\u00E9rents. Elle peut indiquer la pr\u00E9cision d'une valeur approch\u00E9e ou d'une approximation. Par exemple, \u00AB a est une valeur approch\u00E9e de x \u00E0 \u03B5 pr\u00E8s \u00BB signifie que la condition est v\u00E9rifi\u00E9e."@fr , "A\u017E na ... je ust\u00E1len\u00FD matematick\u00FD obrat, kter\u00FDm se vyjad\u0159uje, \u017Ee v dan\u00E9m kontextu lze jednotliv\u00E9 prvky t\u0159\u00EDdy ekvivalence pova\u017Eovat v\u0161echny za jedin\u00FD objekt. Term\u00EDn n\u00E1sleduj\u00EDc\u00ED za a\u017E na ud\u00E1v\u00E1 zanedb\u00E1vanou vlastnost, nebo postup, kter\u00FDm lze mezi sebou p\u0159ev\u00E1d\u011Bt ekvivalentn\u00ED prvky."@cs , "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456 \u0444\u0440\u0430\u0437\u0430 \u00AB\u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E\u00BB \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0434\u043B\u044F \u0432\u0438\u0441\u043B\u043E\u0432\u043B\u0435\u043D\u043D\u044F \u0456\u0434\u0435\u0457 \u043F\u0440\u043E \u0442\u0435, \u0449\u043E \u0434\u0435\u044F\u043A\u0456 \u043E\u0431'\u0454\u043A\u0442\u0438 \u0432 \u043E\u0434\u043D\u043E\u043C\u0443 \u043A\u043B\u0430\u0441\u0456, \u0445\u043E\u0447 \u0456 \u0432\u0456\u0434\u043C\u0456\u043D\u043D\u0456 \u043E\u0434\u0438\u043D \u0432\u0456\u0434 \u043E\u0434\u043D\u043E\u0433\u043E, \u043F\u0440\u043E\u0442\u0435 \u043C\u043E\u0436\u0443\u0442\u044C \u0432\u0432\u0430\u0436\u0430\u0442\u0438\u0441\u044F \u0435\u043A\u0432\u0456\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u0438\u043C\u0438 \u0437\u0430 \u043F\u0435\u0432\u043D\u043E\u0457 \u0443\u043C\u043E\u0432\u0438 \u0430\u0431\u043E \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F. \u0426\u044F \u0444\u0440\u0430\u0437\u0430 \u0447\u0430\u0441\u0442\u043E \u0437'\u044F\u0432\u043B\u044F\u0454\u0442\u044C\u0441\u044F \u0443 \u0434\u0438\u0441\u043A\u0443\u0441\u0456\u044F\u0445 \u043F\u0440\u043E \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0438 \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u0442\u0430 \u0443\u043C\u043E\u0432, \u0437\u0430 \u044F\u043A\u0438\u0445 \u0434\u0435\u044F\u043A\u0456 \u0437 \u0446\u0438\u0445 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u043C\u043E\u0436\u0443\u0442\u044C \u0432\u0432\u0430\u0436\u0430\u0442\u0438\u0441\u044F \u0435\u043A\u0432\u0456\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u0438\u043C\u0438. \u041D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434, \u0434\u043B\u044F \u0434\u0432\u043E\u0445 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 a \u0456 b \u043C\u043D\u043E\u0436\u0438\u043D\u0438 S, \u0432\u0438\u0441\u043B\u0456\u0432 \u00ABa \u0456 b \u0435\u043A\u0432\u0456\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u0456 \u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E X\u00BB \u043E\u0437\u043D\u0430\u0447\u0430\u0454, \u0449\u043E a \u0456 b \u0435\u043A\u0432\u0456\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u0456, \u044F\u043A\u0449\u043E \u043A\u0440\u0438\u0442\u0435\u0440\u0456\u0439 X, \u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434, \u0442\u0430\u043A\u0438\u0439 \u044F\u043A \u043E\u0431\u0435\u0440\u0442\u0430\u043D\u043D\u044F \u0430\u0431\u043E \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043A\u0430 \u0456\u0433\u043D\u043E\u0440\u0443\u0454\u0442\u044C\u0441\u044F. \u0423 \u0446\u044C\u043E\u043C\u0443 \u0432\u0438\u043F\u0430\u0434\u043A\u0443 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0438 S \u043C\u043E\u0436\u0443\u0442\u044C \u0431\u0443\u0442\u0438 \u043F\u0440\u0438\u043F\u0438\u0441\u0430\u043D\u0456 \u0434\u043E \u043F\u0456\u0434\u043C\u043D\u043E\u0436\u0438\u043D, \u0432\u0456\u0434\u043E\u043C\u0438\u0445 \u044F\u043A \u00AB\u043A\u043B\u0430\u0441\u0438 \u0435\u043A\u0432\u0456\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u043E\u0441\u0442\u0456\u00BB \u2014 \u0446\u0435 \u043C\u043D\u043E\u0436\u0438\u043D\u0438, \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0438 \u044F\u043A\u0438\u0445 \u0435\u043A\u0432\u0456\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u0456 \u043E\u0434\u0438\u043D \u043E\u0434\u043D\u043E\u043C\u0443 \u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E X. \u0412 \u0434\u0435\u044F\u043A\u0438\u0445 \u0432\u0438\u043F\u0430\u0434\u043A\u0430\u0445 \u0446\u0435 \u043C\u043E\u0436\u0435 \u043E\u0437\u043D\u0430\u0447\u0430\u0442\u0438, \u0449\u043E a \u0456 b \u043C\u043E\u0436\u0443\u0442\u044C \u0431\u0443\u0442\u0438 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u0456 \u043E\u0434\u0438\u043D \u0432 \u043E\u0434\u043D\u043E\u0433\u043E"@uk , "Two mathematical objects a and b are called equal up to an equivalence relation R \n* if a and b are related by R, that is, \n* if aRb holds, that is, \n* if the equivalence classes of a and b with respect to R are equal. This figure of speech is mostly used in connection with expressions derived from equality, such as uniqueness or count.For example, x is unique up to R means that all objects x under consideration are in the same equivalence class with respect to the relation R."@en , "Em matem\u00E1tica, o termo salvo P, ou a menos que P, descreve a rela\u00E7\u00E3o na que os membros de algum conjunto podem ser vistos como equivalentes para algum prop\u00F3sito. P descreve una propriedade ou processo que transforma um elemento em outro da mesma classe de equival\u00EAncia, ou seja, um que se considera equivalente a ele. Note-se que neste contexto, a express\u00E3o \u00ABsalvo\u00BB n\u00E3o tem um sentido de exce\u00E7\u00E3o ou de exclus\u00E3o, sen\u00E3o pelo contr\u00E1rio, de inclus\u00E3o ou equival\u00EAncia."@pt . @prefix foaf: . dbr:Up_to foaf:depiction , , . @prefix dcterms: . @prefix dbc: . dbr:Up_to dcterms:subject dbc:Mathematical_terminology . @prefix dbo: . dbr:Up_to dbo:wikiPageID 44787 ; dbo:wikiPageRevisionID 1081479299 ; dbo:wikiPageWikiLink dbr:Up_to , dbr:Isomorphism , dbr:Eight_queens_puzzle , dbr:Hyperreal_number , dbr:Permutation , dbr:Tetromino , dbr:Regular_polygon , dbr:Standard_part_function , dbr:All_other_things_being_equal , dbr:Proof_techniques , dbr:Adequality , , dbr:Chessboard , dbr:Bisimulation , dbc:Mathematical_terminology , dbr:Group_theory , , dbr:Infinitesimal , dbr:Quotient_set , dbr:Mathematical_object , dbr:Abuse_of_notation , dbr:Equivalence_classes , , dbr:Quotient_group , , , dbr:Unit_square , dbr:Symmetry , dbr:List_of_mathematical_jargon , , dbr:Synecdoche , dbr:Group_isomorphism , , dbr:Essentially_unique , dbr:Tetris , dbr:Equivalence_relation , , dbr:Rotation ; dbo:wikiPageExternalLink . @prefix owl: . dbr:Up_to owl:sameAs . @prefix wikidata: . dbr:Up_to owl:sameAs wikidata:Q2914964 , , , , , , , , , , . @prefix dbpedia-zh: . dbr:Up_to owl:sameAs dbpedia-zh:Up_to , . @prefix dbpedia-ca: . dbr:Up_to owl:sameAs dbpedia-ca:Llevat_de . @prefix dbp: . @prefix dbt: . dbr:Up_to dbp:wikiPageUsesTemplate dbt:Format_link , dbt:Short_description , dbt:Wiktionary ; dbo:thumbnail ; dbo:abstract "Em matem\u00E1tica, o termo salvo P, ou a menos que P, descreve a rela\u00E7\u00E3o na que os membros de algum conjunto podem ser vistos como equivalentes para algum prop\u00F3sito. P descreve una propriedade ou processo que transforma um elemento em outro da mesma classe de equival\u00EAncia, ou seja, um que se considera equivalente a ele. Note-se que neste contexto, a express\u00E3o \u00ABsalvo\u00BB n\u00E3o tem um sentido de exce\u00E7\u00E3o ou de exclus\u00E3o, sen\u00E3o pelo contr\u00E1rio, de inclus\u00E3o ou equival\u00EAncia."@pt , "\u5728\u6570\u5B66\u9886\u57DF\uFF0C\u8A5E\u7D44\u201Cup to xxx\u201D\u8868\u793A\u4E3A\u4E86\u67D0\u79CD\u76EE\u7684\u540C\u4E00\u7B49\u4EF7\u7C7B\u4E2D\u7684\u5143\u7D20\u89C6\u4E3A\u4E00\u4F53\u3002\u201Cxxxx\u201D\u63CF\u8FF0\u4E86\u67D0\u79CD\u6027\u8D28\u6216\u5C06\u4E2D\u5143\u7D20\u53D8\u4E3A\u540C\u4E00\u7B49\u4EF7\u7C7B\u4E2D\u53E6\u4E00\u4E2A\u7684\u64CD\u4F5C\uFF08\u5373\u5C06\u5143\u7D20\u548C\u5B83\u53D8\u4E3A\u7684\u90A3\u4E2A\u7B49\u4EF7\uFF09\u3002\u4F8B\u5982\u5728\u7FA4\u8BBA\u4E2D\uFF0C\u6211\u4EEC\u6709\u4E00\u4E2A\u7FA4G\u4F5C\u7528\u5728\u96C6\u5408X\u4E0A\uFF0C\u5728\u6B64\u60C5\u5F62\uFF1A\u5982\u679CX\u4E2D\u4E24\u4E2A\u5143\u7D20\u5728\u540C\u4E00\u8F68\u9053\u4E2D\uFF0C\u6211\u4EEC\u53EF\u4EE5\u8BF4\u5B83\u4EEC\u7B49\u4EF7\u201Cup to\u7FA4\u4F5C\u7528\u201D\u3002 \u4E2D\u6587\u4E2D\u6CA1\u6709\u7C7B\u4F3C\u5BF9\u5E94\u7684\u8BCD\u7EC4\uFF0C\u7FFB\u8B6F\u6210\u4E2D\u6587\u6642\uFF0C\u53EF\u4EE5\u659F\u914C\u8B6F\u70BA\uFF1A\u300C\u4E0D\u5225\u22EF\u22EF\u4E4B\u7570\u300D\u3001\u300C\u4E0D\u8FA8\u22EF\u22EF\u4E4B\u5225\u300D\u3001\u201C\u5728xxx\u7684\u610F\u4E49\u4E0B\u201D\u3001\u201C\u5DEE\u4E00\u4E2Axxx\u201D\u7B49\u3002\u6BD4\u5982\u4E0A\u9762\u53EF\u4EE5\u7FFB\u8BD1\u4E3A\u201C\u5DEE\u4E00\u4E2A\u7FA4\u4F5C\u7528\u7684\u610F\u4E49\u4E0B\u7B49\u4EF7\u201D\u3002\u4F46\u662F\uFF0C\u9019\u500B\u7FFB\u8B6F\u662F\u65E2\u8FC2\u8FF4\u53C8\u7B28\u62D9\uFF0C\u56E0\u70BA\u6578\u5B78\u4E2D\u300C\u5728xxx\u7684\u610F\u7FA9\u4E0B\u300D\u901A\u5E38\u662F\u5C0D\u6709\u6578\u500B\u4E0D\u7B49\u50F9\u5B9A\u7FA9\u7684\u8A5E\u8A9E\u6307\u5B9A\u5176\u610F\u7FA9\uFF0C\u5C0D\u61C9\u82F1\u6587\u201Cin the sense of\u201D\uFF0C\u4F8B\u5982\u300C\u9019\u500B\u51FD\u6578\u5728\u52D2\u8C9D\u683C\u7684\u610F\u7FA9\u4E0B\u53EF\u7A4D\uFF0C\u4F46\u662F\u5728\u9ECE\u66FC\u7684\u610F\u7FA9\u4E0B\u4E0D\u53EF\u7A4D\u300D\uFF0C\u5C31\u5C0D\u300C\u53EF\u7A4D\u300D\u4E00\u8A5E\u5148\u5F8C\u6307\u5B9A\u5169\u500B\u4E0D\u7B49\u50F9\u7684\u5B9A\u7FA9\uFF1B\u7136\u800C\uFF0C\u6578\u5B78\u4E2D\u82F1\u6587\u77ED\u8A9E\u201Cup to\u201D\u7684\u91CD\u9EDE\u4E0D\u5728\u78BA\u5B9A\u67D0\u8A5E\u8A9E\u7684\u5B9A\u7FA9\uFF0C\u800C\u5728\u7701\u7565\u6389\u4E00\u4E9B\u975E\u672C\u8CEA\u7684\u6B21\u8981\u5DEE\u7570\u3002"@zh , "En matem\u00E1ticas, el t\u00E9rmino salvo , o a menos de , describe la relaci\u00F3n en la que los miembros de alg\u00FAn conjunto pueden ser vistos como equivalentes para alg\u00FAn prop\u00F3sito. describe una propiedad o proceso que transforma un elemento en otro de la misma clase de equivalencia, es decir, uno que se considera equivalente a \u00E9l. N\u00F3tese que en este contexto, la expres\u00F3n \u00ABsalvo\u00BB no tiene un sentido de excepci\u00F3n o de exclusi\u00F3n, sino por el contrario, de inclusi\u00F3n o equivalencia."@es , "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456 \u0444\u0440\u0430\u0437\u0430 \u00AB\u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E\u00BB \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0434\u043B\u044F \u0432\u0438\u0441\u043B\u043E\u0432\u043B\u0435\u043D\u043D\u044F \u0456\u0434\u0435\u0457 \u043F\u0440\u043E \u0442\u0435, \u0449\u043E \u0434\u0435\u044F\u043A\u0456 \u043E\u0431'\u0454\u043A\u0442\u0438 \u0432 \u043E\u0434\u043D\u043E\u043C\u0443 \u043A\u043B\u0430\u0441\u0456, \u0445\u043E\u0447 \u0456 \u0432\u0456\u0434\u043C\u0456\u043D\u043D\u0456 \u043E\u0434\u0438\u043D \u0432\u0456\u0434 \u043E\u0434\u043D\u043E\u0433\u043E, \u043F\u0440\u043E\u0442\u0435 \u043C\u043E\u0436\u0443\u0442\u044C 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\u0443\u043D\u0456\u043A\u0430\u043B\u044C\u043D\u0430, \u044F\u043A\u0449\u043E \u043C\u0438 \u0456\u0433\u043D\u043E\u0440\u0443\u0454\u043C\u043E \u043F\u043E\u0440\u044F\u0434\u043E\u043A \u043C\u043D\u043E\u0436\u043D\u0438\u043A\u0456\u0432. \u041C\u043E\u0436\u043D\u0430 \u0442\u0430\u043A\u043E\u0436 \u0441\u043A\u0430\u0437\u0430\u0442\u0438, \u0449\u043E \u00AB\u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u044F \u043D\u0435\u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043E\u0433\u043E \u0456\u043D\u0442\u0435\u0433\u0440\u0430\u043B\u0430 , \u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E \u0441\u0442\u0430\u043B\u043E\u0457\u00BB, \u0446\u0435 \u043E\u0437\u043D\u0430\u0447\u0430\u0454, \u0449\u043E \u043E\u0441\u043D\u043E\u0432\u043D\u0430 \u0443\u0432\u0430\u0433\u0430 \u043F\u0440\u0438\u0434\u0456\u043B\u044F\u0454\u0442\u044C\u0441\u044F \u0432\u0438\u0440\u0456\u0448\u0435\u043D\u043D\u044E , \u0430 \u043D\u0435 \u0434\u043E\u0434\u0430\u043D\u0456\u0439 \u043A\u043E\u043D\u0441\u0442\u0430\u043D\u0442\u0456, \u0456 \u0449\u043E \u0434\u043E\u0434\u0430\u0432\u0430\u043D\u043D\u044F \u043A\u043E\u043D\u0441\u0442\u0430\u043D\u0442\u0438 \u0441\u043B\u0456\u0434 \u0440\u043E\u0437\u0433\u043B\u044F\u0434\u0430\u0442\u0438, \u044F\u043A \u0434\u043E\u0434\u0430\u0442\u043A\u043E\u0432\u0443 \u0456\u043D\u0444\u043E\u0440\u043C\u0430\u0446\u0456\u044E. \u041F\u043E\u0434\u0430\u043B\u044C\u0448\u0456 \u043F\u0440\u0438\u043A\u043B\u0430\u0434\u0438 \u043C\u0456\u0441\u0442\u044F\u0442\u044C \u0444\u0440\u0430\u0437\u0438 \u00AB\u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E \u0456\u0437\u043E\u043C\u043E\u0440\u0444\u0456\u0437\u043C\u0443\u00BB, \u00AB\u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043A\u0438\u00BB \u0456 \u00AB\u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E \u043E\u0431\u0435\u0440\u0442\u0430\u043D\u044C\u00BB, \u044F\u043A\u0456 \u043E\u043F\u0438\u0441\u0430\u043D\u0456 \u0432 \u0440\u043E\u0437\u0434\u0456\u043B\u0456 \u043F\u0440\u0438\u043A\u043B\u0430\u0434\u0456\u0432. \u0423 \u043D\u0435\u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0438\u0445 \u043A\u043E\u043D\u0442\u0435\u043A\u0441\u0442\u0430\u0445, \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438 \u0447\u0430\u0441\u0442\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u044E\u0442\u044C \u0441\u043B\u043E\u0432\u043E \u043F\u043E \u043C\u043E\u0434\u0443\u043B\u044E (\u0430\u0431\u043E \u043F\u0440\u043E\u0441\u0442\u043E \u00ABmod\u00BB) \u0434\u043B\u044F \u0430\u043D\u0430\u043B\u043E\u0433\u0456\u0447\u043D\u0438\u0445 \u0446\u0456\u043B\u0435\u0439, \u044F\u043A \u00AB\u0456\u0437\u043E\u043C\u043E\u0440\u0444\u0456\u0437\u043C \u043F\u043E \u043C\u043E\u0434\u0443\u043B\u044E\u00BB."@uk , "En math\u00E9matiques, l'expression \u00AB \u00E0 quelque chose pr\u00E8s \u00BB peut avoir plusieurs sens diff\u00E9rents. Elle peut indiquer la pr\u00E9cision d'une valeur approch\u00E9e ou d'une approximation. Par exemple, \u00AB a est une valeur approch\u00E9e de x \u00E0 \u03B5 pr\u00E8s \u00BB signifie que la condition est v\u00E9rifi\u00E9e. Elle peut aussi signifier que des \u00E9l\u00E9ments d'une certaine classe d'\u00E9quivalence doivent \u00EAtre consid\u00E9r\u00E9s comme ne faisant qu'un. Dans l'expression \u00E0 xxx pr\u00E8s, xxx repr\u00E9sente alors une propri\u00E9t\u00E9 ou un processus qui transforment un \u00E9l\u00E9ment en un autre de la m\u00EAme classe d'\u00E9quivalence, c'est-\u00E0-dire en un \u00E9l\u00E9ment qui est consid\u00E9r\u00E9 comme \u00E9quivalent au premier. En th\u00E9orie des groupes par exemple, nous pouvons avoir un groupe G agissant sur un ensemble X, auquel cas on peut dire que deux \u00E9l\u00E9ments de X sont \u00E9quivalents \u00AB \u00E0 l'action de groupe pr\u00E8s \u00BB, s'ils appartiennent \u00E0 la m\u00EAme orbite."@fr , "\u6570\u5B66\u306E\u6587\u8108\u306B\u304A\u3051\u308B\u300C\u2014\uFF08\u306E\u9055\u3044\uFF09\u3092\u9664\u3044\u3066\u2026\u300D (\u306E\u3061\u304C\u3044\u3092\u306E\u305E\u3044\u3066\u3001\u2026 \"up to\" \u2014) \u3068\u3044\u3046\u8A9E\u53E5\u306F\u3001\u300C\u2014 \u306B\u95A2\u3059\u308B\u5DEE\u7570\u3092\u7121\u8996\u3059\u308B\u300D\u3053\u3068\u3092\u610F\u5473\u3059\u308B\u5C02\u9580\u7528\u8A9E\u3067\u3042\u308B\u3002\u3053\u306E\u8A00\u3044\u56DE\u3057\u306E\u610F\u5473\u3059\u308B\u3068\u3053\u308D\u306F\u3001\u300C\u9069\u5F53\u306A\u76EE\u7684\u306E\u3082\u3068\u3067\u306F\u3001\u3042\u308B\u3072\u3068\u3064\u306E\u540C\u5024\u985E\u306B\u5C5E\u3059\u308B\u5143\u5168\u4F53\u3092\u3001\u4F55\u304B\u5358\u4E00\u306E\u5B9F\u4F53\u3092\u8868\u3059\u3082\u306E\u3068\u307F\u306A\u305B\u308B\u300D\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308B\u3002\"\u2014\" \u306E\u90E8\u5206\u306B\u306F\u3001\u4F55\u3089\u304B\u306E\u6027\u8CEA\u3084\u3001\u540C\u3058\u540C\u5024\u985E\u306B\u5C5E\u3059\u308B\u5143(\u3064\u307E\u308A\u4E00\u65B9\u306F\u4ED6\u65B9\u306B\u540C\u5024\u3068\u306A\u308B\u3088\u3046\u306A\u5143)\u306E\u9593\u306E\u5909\u63DB\u306E\u904E\u7A0B\u3092\u8A18\u8FF0\u3059\u308B\u5185\u5BB9\u304C\u5165\u308B\u3002 \u305F\u3068\u3048\u3070\u4E0D\u5B9A\u7A4D\u5206\u3092\u8A08\u7B97\u3059\u308B\u3068\u304D\u3001\u305D\u306E\u7D50\u679C\u306F\u300C\u5B9A\u6570\u9805\u306E\u9055\u3044\u3092\u9664\u3044\u3066\u300D f\u2009(x) \u3067\u3042\u308B\u3068\u3044\u3046\u3088\u3046\u306B\u8A00\u3046\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u305D\u306E\u610F\u5473\u306F\u3001f\u2009(x) \u4EE5\u5916\u306B\u4E0D\u5B9A\u7A4D\u5206 g(x) \u304C\u3042\u3063\u305F\u3068\u3057\u3066\u3082 g(x) = f\u2009(x) + C (C \u306F\u5B9A\u6570)\u3068\u66F8\u304F\u3053\u3068\u304C\u3067\u304D\u3001\u305D\u306E\u5F8C\u306E\u8AD6\u7406\u5C55\u958B\u306B\u304A\u3044\u3066 f \u306E\u304B\u308F\u308A\u306B g \u3092\u7528\u3044\u3066\u3082\u5F71\u97FF\u304C\u306A\u3044\u3053\u3068\u3092\u793A\u5506\u3057\u3066\u3044\u308B\u3002\u307E\u305F\u4F8B\u3048\u3070\u7FA4\u8AD6\u3067\u3001\u7FA4 G \u304C X \u306B\u4F5C\u7528\u3059\u308B\u3068\u304D\u3001X \u306E\u3075\u305F\u3064\u306E\u5143\u304C\u540C\u3058\u306B\u5C5E\u3059\u308B\u306A\u3089\u3070\u3001\u305D\u308C\u3089\u306F\u300C\u7FA4\u4F5C\u7528\u306E\u9055\u3044\u3092\u9664\u3044\u3066\u300D\u540C\u5024\u3067\u3042\u308B\u3068\u8A00\u3044\u8868\u3059\u3053\u3068\u304C\u3067\u304D\u308B\u3002 \u6CE8: \u5C11\u3057\u7815\u3051\u305F\u8A00\u3044\u65B9\u3068\u3044\u3046\u3053\u3068\u306B\u306F\u306A\u308B\u304C\u3001\u540C\u3058\u76EE\u7684\u3067\u300C\u2014 \u3067\u5272\u3063\u3066\u300D\u300C\u2014 \u3092\u6CD5\u3068\u3057\u3066\u300D(modulo \u2014, mod \u2014) \u3068\u8A00\u3044\u56DE\u3059\u3053\u3068\u3082\u3088\u304F\u884C\u308F\u308C\u308B\u3002\u4EE5\u4E0B\u306B\u6319\u3052\u308B\u4F8B\u3067\u3042\u308C\u3070\u3001\u300C\u4F4D\u6570 4 \u306E\u7FA4\u306F\u540C\u578B\u3067\u5272\u308C\u3070\uFF08mod \u540C\u578B\u3067\uFF092\u7A2E\u985E\u3067\u3042\u308B\u300D\u3068\u304B\u3001\u300C\u30AF\u30A4\u30FC\u30F3\u306E\u540D\u524D\u3092\u6CD5\u3068\u3057\u306692\u500B\u306E\u89E3\u304C\u3042\u308B\u300D\u3068\u3044\u3063\u305F\u5177\u5408\u3067\u3042\u308B\u3002\u3053\u306E\u8A00\u3044\u56DE\u3057\u306F\u5408\u540C\u7B97\u8853\u306B\u304A\u3051\u308B\u300C7 \u3068 11 \u3068\u306F 4 \u3092\u6CD5\u3068\u3057\u3066(\u3042\u308B\u3044\u306F 4 \u3067\u5272\u3063\u305F\u4F59\u308A\u304C)\u7B49\u3057\u3044\u300D\u3068\u3044\u3046\u3088\u3046\u306A\u69CB\u6587\u306E\u6D41\u7528\u3067\u3042\u308B\uFF08\u3082\u3061\u308D\u3093\u3001\u805E\u304D\u624B\u304C\u3053\u3046\u3044\u3063\u305F\u7565\u5F0F\u306E\u6570\u5B66\u7528\u8A9E\u306B\u6163\u308C\u3066\u3044\u308B\u3053\u3068\u304C\u524D\u63D0\uFF09\u3002"@ja , "Two mathematical objects a and b are called equal up to an equivalence relation R \n* if a and b are related by R, that is, \n* if aRb holds, that is, \n* if the equivalence classes of a and b with respect to R are equal. This figure of speech is mostly used in connection with expressions derived from equality, such as uniqueness or count.For example, x is unique up to R means that all objects x under consideration are in the same equivalence class with respect to the relation R. Moreover, the equivalence relation R is often designated rather implicitly by a generating condition or transformation.For example, the statement \"an integer's prime factorization is unique up to ordering\" is a concise way to say that any two lists of prime factors of a given integer are equivalent with respect to the relation R that relates two lists if one can be obtained by reordering (permutation) from the other. As another example, the statement \"the solution to an indefinite integral is sin(x), up to addition by a constant\" tacitly employs the equivalence relation R between functions, defined by fRg if f\u2212g is a constant function, and means that the solution and the function sin(x) are equal up to this R.In the picture, \"there are 4 partitions up to rotation\" means that the set P has 4 equivalence classes with respect to R defined by aRb if b can be obtained from a by rotation; one representative from each class is shown in the bottom left picture part. Equivalence relations are often used to disregard possible differences of objects, so \"up to R\" can be understood informally as \"ignoring the same subtleties as R does\".In the factorization example, \"up to ordering\" means \"ignoring the particular ordering\". Further examples include \"up to isomorphism\", \"up to permutations\", and \"up to rotations\", which are described in the Examples section. In informal contexts, mathematicians often use the word modulo (or simply \"mod\") for similar purposes, as in \"modulo isomorphism\"."@en , "A\u017E na ... je ust\u00E1len\u00FD matematick\u00FD obrat, kter\u00FDm se vyjad\u0159uje, \u017Ee v dan\u00E9m kontextu lze jednotliv\u00E9 prvky t\u0159\u00EDdy ekvivalence pova\u017Eovat v\u0161echny za jedin\u00FD objekt. Term\u00EDn n\u00E1sleduj\u00EDc\u00ED za a\u017E na ud\u00E1v\u00E1 zanedb\u00E1vanou vlastnost, nebo postup, kter\u00FDm lze mezi sebou p\u0159ev\u00E1d\u011Bt ekvivalentn\u00ED prvky."@cs , "En matem\u00E0tiques, el terme llevat de indica que l'objecte gramatical \u00E9s una classe d'equival\u00E8ncia, que hom ha de considerar com una entitat simple. Si aquest objecte \u00E9s una classe de transformacions (com per exemple \"isomorfisme\" o \"permutaci\u00F3\"), aix\u00F2 implica l'equival\u00E8ncia d'objectes, un dels quals \u00E9s la imatge de l'altre per aquesta transformaci\u00F3. Si X \u00E9s una propietat o un proc\u00E9s, el terme \"llevat de X\" vol dir \"descartant una possible difer\u00E8ncia en X\". Per exemple, podem tenir l'afirmaci\u00F3 \"la factoritzaci\u00F3 en nombres primers d'un enter \u00E9s \u00FAnica llevat d'ordenacions\", la qual cosa vol dir que la factoritzaci\u00F3 en nombres primers \u00E9s \u00FAnica si no tenim en compte l'ordre dels factors; o tamb\u00E9 podem dir que \"la soluci\u00F3 a una integral indefinida \u00E9s f(x), llevat de sumar una constant\", la qual cosa vol dir que la constant sumada no \u00E9s l'objecte d'estudi, sin\u00F3 la soluci\u00F3 f(x), i que l'addici\u00F3 de la constant \u00E9s un objectiu secundari d'estudi. En tenim altres exemples a les expressions llevat d'isomorfisme, llevat de permutacions o llevat de rotacions, que veurem m\u00E9s endavant. En contextos informals, els matem\u00E0tics acostumen a emprar el terme m\u00F2dul (o simplement \"mod\") per prop\u00F2sits similars, com per exemple \"m\u00F2dul un isomorfisme\"."@ca . @prefix prov: . dbr:Up_to prov:wasDerivedFrom . @prefix xsd: . dbr:Up_to dbo:wikiPageLength "7374"^^xsd:nonNegativeInteger . @prefix wikipedia-en: . dbr:Up_to foaf:isPrimaryTopicOf wikipedia-en:Up_to .