@prefix rdf: . @prefix dbr: . @prefix yago: . dbr:Dyadic_rational rdf:type yago:Relation100031921 , yago:WikicatFractions , yago:Fraction114922107 , yago:RationalNumber113730469 , yago:Measure100033615 , yago:Chemical114806838 , yago:Part113809207 , yago:Abstraction100002137 , yago:PhysicalEntity100001930 , yago:Material114580897 , yago:WikicatRationalNumbers , yago:ComplexNumber113729428 , yago:RealNumber113729902 , yago:Matter100020827 , yago:Substance100019613 , yago:Number113582013 , yago:DefiniteQuantity113576101 . @prefix rdfs: . dbr:Dyadic_rational rdfs:label "\u0414\u0432\u043E\u0438\u0447\u043D\u043E-\u0440\u0430\u0446\u0438\u043E\u043D\u0430\u043B\u044C\u043D\u043E\u0435 \u0447\u0438\u0441\u043B\u043E"@ru , "Dyadic rational"@en , "Racional di\u00E1dico"@es , "Frazione diadica"@it , "\u0414\u0432\u0456\u0439\u043A\u043E\u0432\u043E-\u0440\u0430\u0446\u0456\u043E\u043D\u0430\u043B\u044C\u043D\u0435 \u0447\u0438\u0441\u043B\u043E"@uk , "\u4E8C\u8FDB\u5206\u6570"@zh , "\uC774\uC9C4 \uC720\uB9AC\uC218"@ko , "Dyadiskt br\u00E5k"@sv , "Fraction dyadique"@fr , "Fra\u00E7\u00E3o di\u00E1dica"@pt , "Dyadick\u00FD zlomek"@cs ; rdfs:comment "Dyadick\u00FD zlomek je v matematice ozna\u010Den\u00ED pro takov\u00E9 racion\u00E1ln\u00ED \u010D\u00EDslo, jeho\u017E zlomek v z\u00E1kladn\u00EDm tvaru, tedy p\u0159i nesoud\u011Blnosti \u010Ditatele a jmenovatele, m\u00E1 v jmenovateli . Tedy takov\u00FD zlomek , kde a jsou cel\u00E1 \u010D\u00EDsla."@cs , "\u0414\u0432\u0456\u0439\u043A\u043E\u0432\u043E-\u0440\u0430\u0446\u0456\u043E\u043D\u0430\u043B\u044C\u043D\u0456 \u0447\u0438\u0441\u043B\u0430 \u2014 \u0440\u0430\u0446\u0456\u043E\u043D\u0430\u043B\u044C\u043D\u0456 \u0447\u0438\u0441\u043B\u0430, \u0437\u043D\u0430\u043C\u0435\u043D\u043D\u0438\u043A \u044F\u043A\u0438\u0445 \u0454 \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u043C \u0434\u0432\u0456\u0439\u043A\u0438. \u0406\u043D\u0430\u043A\u0448\u0435 \u043A\u0430\u0436\u0443\u0447\u0438, \u0447\u0438\u0441\u043B\u0430 \u0432\u0438\u0434\u0443 , \u0434\u0435 \u0446\u0456\u043B\u0435 \u0447\u0438\u0441\u043B\u043E, \u0430 \u043D\u0430\u0442\u0443\u0440\u0430\u043B\u044C\u043D\u0435. \u041D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434, 1/2 \u0456 3/8 \u0434\u0432\u0456\u0439\u043A\u043E\u0432\u043E-\u0440\u0430\u0446\u0456\u043E\u043D\u0430\u043B\u044C\u043D\u0456, \u0430 1/3 \u2014 \u043D\u0456. \u0421\u0430\u043C\u0435 \u0446\u0456 \u0447\u0438\u0441\u043B\u0430 \u043C\u0430\u044E\u0442\u044C \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0435 \u043F\u043E\u0434\u0430\u043D\u043D\u044F \u0432 \u0434\u0432\u0456\u0439\u043A\u043E\u0432\u0456\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u0456 \u0447\u0438\u0441\u043B\u0435\u043D\u043D\u044F."@uk , "In matematica, una frazione diadica - o razionale diadico - \u00E8 un numero razionale espresso sotto forma di frazione, il denominatore della quale \u00E8 una potenza di 2. Quindi un numero del tipo Questi numeri hanno la propriet\u00E0 di avere una espansione diadica finita. L'insieme dei numeri razionali diadici \u00E8 denso in : ogni numero reale pu\u00F2 essere approssimato arbitrariamente dalla frazione diadica"@it , "En math\u00E9matiques, une fraction dyadique ou rationnel dyadique est un nombre rationnel qui peut s'\u00E9crire sous forme de fraction avec pour d\u00E9nominateur une puissance de deux. On peut noter l'ensemble des nombres dyadiques formellement par Par exemple, 1/2 ou 3/8 sont des fractions dyadiques, mais pas 1/3. De m\u00EAme que les nombres d\u00E9cimaux sont les nombres qui ont un d\u00E9veloppement d\u00E9cimal fini, les fractions dyadiques sont les nombres qui ont un d\u00E9veloppement binaire fini. La somme, la diff\u00E9rence ou le produit de deux fractions dyadiques quelconques est elle-m\u00EAme une fraction dyadique :"@fr , "Para cualquier n\u00FAmero primo dado , una fracci\u00F3n p -\u00E1dica o p -\u00E1dica racional es un n\u00FAmero racional cuyo denominador, cuando la raz\u00F3n est\u00E1 en t\u00E9rminos m\u00EDnimos (coprimos), es una potencia de , es decir, un n\u00FAmero de la forma donde a es un n\u00FAmero entero y b es un n\u00FAmero natural. Estos son precisamente los n\u00FAmeros que poseen una base finita - expansi\u00F3n del sistema num\u00E9rico posicional p. Cuando , se denominan fracciones di\u00E1dicas o racionales di\u00E1dicas; por ejemplo, 1/2 o 3/8, pero no 1/3."@es , "Em matem\u00E1tica, uma fra\u00E7\u00E3o di\u00E1dica ou racional di\u00E1dico \u00E9 um n\u00FAmero racional cujo denominador \u00E9 uma pot\u00EAncia de dois, ou seja, um n\u00FAmero da forma onde a \u00E9 um n\u00FAmero inteiro e b \u00E9 um n\u00FAmero natural; por exemplo, 1/2 ou 3/8, mas n\u00E3o 1/3. Estes s\u00E3o precisamente os n\u00FAmeros cuja expans\u00E3o bin\u00E1ria \u00E9 finita."@pt , "\u4E8C\u8FDB\u5206\u6570\uFF0C\u4E5F\u79F0\u4E3A\u4E8C\u8FDB\u6709\u7406\u6570\uFF0C\u662F\u4E00\u79CD\u5206\u6BCD\u662F2\u7684\u5E42\u7684\u5206\u6570\u3002\u53EF\u4EE5\u8868\u793A\u6210\uFF0C\u5176\u4E2D\uFF0C\u662F\u4E00\u4E2A\u6574\u6570\uFF0C\u662F\u4E00\u4E2A\u81EA\u7136\u6570\u3002\u4F8B\u5982\uFF1A\uFF0C\uFF0C\u800C\u5C31\u4E0D\u662F\u3002(\u82F1\u5236\u5355\u4F4D\u4E2D\u5E7F\u6CDB\u91C7\u7528\u4E8C\u8FDB\u5206\u6570\uFF0C\u4F8B\u5982\u82F1\u5BF8\uFF0C\u82F1\u5BF8\uFF0C\u78C5\u3002) \u6240\u6709\u4E8C\u8FDB\u5206\u6570\u7EC4\u6210\u7684\u96C6\u5408\u5728\u5B9E\u6570\u8F74\u4E0A\u662F\u7A20\u5BC6\u7684\uFF1A\u4EFB\u4F55\u5B9E\u6570\u90FD\u53EF\u4EE5\u7528\u5F62\u4E3A\u7684\u4E8C\u8FDB\u5206\u6570\u65E0\u9650\u903C\u8FD1\u3002\u4E0E\u5B9E\u6570\u8F74\u4E0A\u7684\u5176\u5B83\u7A20\u5BC6\u96C6\uFF0C\u4F8B\u5982\u6709\u7406\u6570\u76F8\u6BD4\uFF0C\u4E8C\u8FDB\u5206\u6570\u662F\u76F8\u5BF9\u201C\u5C0F\u201D\u7684\u7A20\u5BC6\u96C6\uFF0C\u8FD9\u5C31\u662F\u4E3A\u4EC0\u4E48\u5B83\u4EEC\u6709\u65F6\u51FA\u73B0\u5728\u8BC1\u660E\u4E2D\uFF08\u4F8B\u5982\u4E4C\u96F7\u677E\u5F15\u7406\uFF09\u3002 \u4EFB\u4F55\u4E24\u4E2A\u4E8C\u8FDB\u5206\u6570\u7684\u548C\u3001\u79EF\uFF0C\u4E0E\u5DEE\u4E5F\u662F\u4E8C\u8FDB\u5206\u6570\uFF1A \u4F46\u662F\uFF0C\u4E24\u4E2A\u4E8C\u8FDB\u5206\u6570\u7684\u5546\u5219\u4E00\u822C\u4E0D\u662F\u4E8C\u8FDB\u5206\u6570\u3002\u56E0\u6B64\uFF0C\u4E8C\u8FDB\u5206\u6570\u5F62\u6210\u4E86\u6709\u7406\u6570\u7684\u4E00\u4E2A\u5B50\u73AF\u3002"@zh , "Dyadiska br\u00E5k \u00E4r inom matematiken rationella tal som utg\u00F6rs av ett br\u00E5k med ett heltal i t\u00E4ljaren och en tv\u00E5potens av ett naturligt tal i n\u00E4mnaren. Dyadiska br\u00E5k kan allts\u00E5 skrivas: d\u00E4r \u00E4r ett heltal, och \u00E4r ett naturligt tal. Exempelvis \u00E4r och (=) dyadiska br\u00E5k, men d\u00E4remot inte ."@sv , "\uC218\uD559\uC5D0\uC11C \uC774\uC9C4 \uC720\uB9AC\uC218(\u4E8C\u9032\u6709\u7406\u6578, dyadic rational) \uB610\uB294 \uC774\uC9C4 \uBD84\uC218(\u4E8C\u9032\u5206\u6578, dyadic fraction)\uB294 \uC774\uC9C4\uBC95 \uC804\uAC1C\uAC00 \uC720\uD55C\uD55C \uC720\uB9AC\uC218\uC774\uB2E4. \uC989, \uBD84\uC790\uAC00 \uC815\uC218, \uBD84\uBAA8\uAC00 2\uC758 \uAC70\uB4ED\uC81C\uACF1\uC778 \uBD84\uC218\uB85C \uB098\uD0C0\uB0BC \uC218 \uC788\uB294 \uC720\uB9AC\uC218\uC774\uB2E4. \uC608\uB97C \uB4E4\uC5B4, 1/2, 3/8\uC740 \uC774\uC9C4 \uC720\uB9AC\uC218\uC774\uBA70, 1/3\uC740 \uC774\uC9C4 \uC720\uB9AC\uC218\uAC00 \uC544\uB2C8\uB2E4."@ko , "In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number."@en , "\u0414\u0432\u043E\u0438\u0447\u043D\u043E-\u0440\u0430\u0446\u0438\u043E\u043D\u0430\u043B\u044C\u043D\u044B\u0435 \u0447\u0438\u0441\u043B\u0430 \u2014 \u0440\u0430\u0446\u0438\u043E\u043D\u0430\u043B\u044C\u043D\u044B\u0435 \u0447\u0438\u0441\u043B\u0430, \u0437\u043D\u0430\u043C\u0435\u043D\u0430\u0442\u0435\u043B\u044C \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u0435\u0442 \u0441\u043E\u0431\u043E\u0439 \u0441\u0442\u0435\u043F\u0435\u043D\u044C \u0434\u0432\u043E\u0439\u043A\u0438. \u0418\u043D\u0430\u0447\u0435 \u0433\u043E\u0432\u043E\u0440\u044F, \u0447\u0438\u0441\u043B\u0430 \u0432\u0438\u0434\u0430 , \u0433\u0434\u0435 \u0446\u0435\u043B\u043E\u0435 \u0447\u0438\u0441\u043B\u043E, \u0430 \u043D\u0430\u0442\u0443\u0440\u0430\u043B\u044C\u043D\u043E\u0435. \u041D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, 1/2 \u0438 3/8 \u0434\u0432\u043E\u0438\u0447\u043D\u043E-\u0440\u0430\u0446\u0438\u043E\u043D\u0430\u043B\u044C\u043D\u044B, \u0430 1/3 \u043D\u0435\u0442. \u0418\u043C\u0435\u043D\u043D\u043E \u044D\u0442\u0438 \u0447\u0438\u0441\u043B\u0430 \u0438\u043C\u0435\u044E\u0442 \u043A\u043E\u043D\u0435\u0447\u043D\u044B\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u044F \u0432 \u0434\u0432\u043E\u0438\u0447\u043D\u043E\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u0435 \u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u044F."@ru . @prefix foaf: . dbr:Dyadic_rational foaf:depiction , , , , , . @prefix dcterms: . @prefix dbc: . dbr:Dyadic_rational dcterms:subject dbc:Ring_theory , dbc:Number_theory , dbc:Rational_numbers , . @prefix dbo: . dbr:Dyadic_rational dbo:wikiPageID 56263 ; dbo:wikiPageRevisionID 1123375333 ; dbo:wikiPageWikiLink dbr:Rational_number , dbr:Presentation_of_a_group , dbr:Order_type , dbr:Real_line , dbr:Inch , , dbr:Time_signature , dbr:Half-integer , , , dbr:Fixed-point_arithmetic , dbr:The_Rite_of_Spring , , dbr:Thompson_groups , dbr:Interval_arithmetic , dbr:Function_composition , dbr:Fractional_part , dbr:Addition , dbr:Power_of_two , dbr:Diagonal_morphism , dbr:Group_homomorphism , , dbr:Bijection , dbr:Homeomorphism , dbr:Real_number , , , dbr:IEEE_floating_point , , dbr:Surreal_number , dbc:Ring_theory , dbr:Indecomposable_continuum , dbr:Wavelet , , dbr:Floor_function , dbr:Computer_science , dbr:Subring , dbr:Binary_number , , dbr:Gallon , , dbr:Multiplication , , , dbr:Complex_number , dbr:Denominator , dbr:Order_isomorphism , dbr:Simple_group , dbr:Quart , dbr:Abelian_group , , dbr:Unary_numeral_system , dbr:Pint , dbr:Reverse_mathematics , dbr:Localization_of_a_ring , dbr:Well-order , dbr:Binary_representation , dbr:Quotient_group , dbr:Pontryagin_duality , dbr:Combinatorial_game_theory , dbr:Indus_Valley_civilisation , dbr:Mathematical_analysis , dbr:Piecewise_linear_function , dbr:Protorus , dbr:Topological_group , dbr:Fusible_number , dbc:Number_theory , dbr:Integer , dbr:Second-order_arithmetic , dbc:Rational_numbers , dbr:P-adic_number , dbr:Peano_arithmetic , dbr:Dense_set , , dbr:Dense_order , dbr:Random_variable , dbr:Whole_note , dbr:Computable_number , , dbr:Floating-point_arithmetic , dbr:Overring , dbr:Musical_notation , dbr:Daubechies_wavelet , dbr:Subtraction , dbr:Igor_Stravinski , dbr:Fractal , dbr:Unit_interval , , dbr:Fraction , , dbr:Jean_Piaget . @prefix owl: . @prefix yago-res: . dbr:Dyadic_rational owl:sameAs yago-res:Dyadic_rational , . @prefix dbpedia-fr: . dbr:Dyadic_rational owl:sameAs dbpedia-fr:Fraction_dyadique . @prefix wikidata: . dbr:Dyadic_rational owl:sameAs wikidata:Q2281400 , , , , , , , , , , . @prefix dbpedia-it: . dbr:Dyadic_rational owl:sameAs dbpedia-it:Frazione_diadica , . @prefix dbp: . @prefix dbt: . dbr:Dyadic_rational dbp:wikiPageUsesTemplate dbt:CSS_image_crop , dbt:Rational_numbers , dbt:Reflist , dbt:Short_description , dbt:Good_article , dbt:Multiple_image , dbt:Music , dbt:Ring_theory_sidebar , dbt:R , dbt:Fractions_and_ratios ; dbo:thumbnail ; dbp:alt "Graph of the question mark function"@en , "Photo of metal disks used as kitchen weights"@en , "Graph of the scaling and wavelet functions of Daubechies' wavelet"@en ; dbp:bsize 427 ; dbp:caption "Minkowski's question-mark function maps rational numbers to dyadic rationals"@en , "A Daubechies wavelet, showing points of non-smoothness at dyadic rationals"@en ; dbp:cheight 256 ; dbp:cwidth 256 ; dbp:description "down to 1/64 lb"@en . @prefix dbd: . dbr:Dyadic_rational dbp:description "2.0"^^dbd:pound , "Kitchen weights measuring dyadic fractions of a pound from"@en ; dbp:image "Minkowski question mark.svg"@en , "Daubechies4-functions.svg"@en ; dbp:oleft 165 ; dbp:otop 27 ; dbp:totalWidth 480 ; dbo:abstract "In matematica, una frazione diadica - o razionale diadico - \u00E8 un numero razionale espresso sotto forma di frazione, il denominatore della quale \u00E8 una potenza di 2. Quindi un numero del tipo Questi numeri hanno la propriet\u00E0 di avere una espansione diadica finita. L'insieme dei numeri razionali diadici \u00E8 denso in : ogni numero reale pu\u00F2 essere approssimato arbitrariamente dalla frazione diadica"@it , "Para cualquier n\u00FAmero primo dado , una fracci\u00F3n p -\u00E1dica o p -\u00E1dica racional es un n\u00FAmero racional cuyo denominador, cuando la raz\u00F3n est\u00E1 en t\u00E9rminos m\u00EDnimos (coprimos), es una potencia de , es decir, un n\u00FAmero de la forma donde a es un n\u00FAmero entero y b es un n\u00FAmero natural. Estos son precisamente los n\u00FAmeros que poseen una base finita - expansi\u00F3n del sistema num\u00E9rico posicional p. Cuando , se denominan fracciones di\u00E1dicas o racionales di\u00E1dicas; por ejemplo, 1/2 o 3/8, pero no 1/3."@es , "Dyadick\u00FD zlomek je v matematice ozna\u010Den\u00ED pro takov\u00E9 racion\u00E1ln\u00ED \u010D\u00EDslo, jeho\u017E zlomek v z\u00E1kladn\u00EDm tvaru, tedy p\u0159i nesoud\u011Blnosti \u010Ditatele a jmenovatele, m\u00E1 v jmenovateli . Tedy takov\u00FD zlomek , kde a jsou cel\u00E1 \u010D\u00EDsla."@cs , "\uC218\uD559\uC5D0\uC11C \uC774\uC9C4 \uC720\uB9AC\uC218(\u4E8C\u9032\u6709\u7406\u6578, dyadic rational) \uB610\uB294 \uC774\uC9C4 \uBD84\uC218(\u4E8C\u9032\u5206\u6578, dyadic fraction)\uB294 \uC774\uC9C4\uBC95 \uC804\uAC1C\uAC00 \uC720\uD55C\uD55C \uC720\uB9AC\uC218\uC774\uB2E4. \uC989, \uBD84\uC790\uAC00 \uC815\uC218, \uBD84\uBAA8\uAC00 2\uC758 \uAC70\uB4ED\uC81C\uACF1\uC778 \uBD84\uC218\uB85C \uB098\uD0C0\uB0BC \uC218 \uC788\uB294 \uC720\uB9AC\uC218\uC774\uB2E4. \uC608\uB97C \uB4E4\uC5B4, 1/2, 3/8\uC740 \uC774\uC9C4 \uC720\uB9AC\uC218\uC774\uBA70, 1/3\uC740 \uC774\uC9C4 \uC720\uB9AC\uC218\uAC00 \uC544\uB2C8\uB2E4."@ko , "Dyadiska br\u00E5k \u00E4r inom matematiken rationella tal som utg\u00F6rs av ett br\u00E5k med ett heltal i t\u00E4ljaren och en tv\u00E5potens av ett naturligt tal i n\u00E4mnaren. Dyadiska br\u00E5k kan allts\u00E5 skrivas: d\u00E4r \u00E4r ett heltal, och \u00E4r ett naturligt tal. Exempelvis \u00E4r och (=) dyadiska br\u00E5k, men d\u00E4remot inte ."@sv , "In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number. The sum, difference, or product of any two dyadic rational numbers is another dyadic rational number, given by a simple formula. However, division of one dyadic rational number by another does not always produce a dyadic rational result. Mathematically, this means that the dyadic rational numbers form a ring, lying between the ring of integers and the field of rational numbers. This ring may be denoted . In advanced mathematics, the dyadic rational numbers are central to the constructions of the dyadic solenoid, Minkowski's question-mark function, Daubechies wavelets, Thompson's group, Pr\u00FCfer 2-group, surreal numbers, and fusible numbers. These numbers are order-isomorphic to the rational numbers; they form a subsystem of the 2-adic numbers as well as of the reals, and can represent the fractional parts of 2-adic numbers. Functions from natural numbers to dyadic rationals have been used to formalize mathematical analysis in reverse mathematics."@en , "Em matem\u00E1tica, uma fra\u00E7\u00E3o di\u00E1dica ou racional di\u00E1dico \u00E9 um n\u00FAmero racional cujo denominador \u00E9 uma pot\u00EAncia de dois, ou seja, um n\u00FAmero da forma onde a \u00E9 um n\u00FAmero inteiro e b \u00E9 um n\u00FAmero natural; por exemplo, 1/2 ou 3/8, mas n\u00E3o 1/3. Estes s\u00E3o precisamente os n\u00FAmeros cuja expans\u00E3o bin\u00E1ria \u00E9 finita."@pt , "En math\u00E9matiques, une fraction dyadique ou rationnel dyadique est un nombre rationnel qui peut s'\u00E9crire sous forme de fraction avec pour d\u00E9nominateur une puissance de deux. On peut noter l'ensemble des nombres dyadiques formellement par Par exemple, 1/2 ou 3/8 sont des fractions dyadiques, mais pas 1/3. De m\u00EAme que les nombres d\u00E9cimaux sont les nombres qui ont un d\u00E9veloppement d\u00E9cimal fini, les fractions dyadiques sont les nombres qui ont un d\u00E9veloppement binaire fini. Le pouce est habituellement divis\u00E9 de mani\u00E8re dyadique plut\u00F4t qu'en fractions d\u00E9cimales ; de mani\u00E8re similaire, les divisions habituelles du gallon en demi-gallons, quarts et pintes sont dyadiques.Les anciens \u00E9gyptiens utilisaient aussi les fractions dyadiques dans les mesures, avec le num\u00E9rateur 1 et des d\u00E9nominateurs allant jusqu'\u00E0 64. L'ensemble de toutes les fractions dyadiques est dense dans l'ensemble des nombres r\u00E9els ; un nombre r\u00E9el quelconque x est limite de la suite de rationnels dyadiques \u230A2nx\u230B/2n. Compar\u00E9 aux autres sous-ensembles denses de la droite r\u00E9elle, tels que les nombres rationnels, c'est un ensemble plut\u00F4t \u00AB petit \u00BB en un certain sens, c'est pourquoi il appara\u00EEt quelquefois dans les d\u00E9monstrations de topologie comme le lemme d'Urysohn. La somme, la diff\u00E9rence ou le produit de deux fractions dyadiques quelconques est elle-m\u00EAme une fraction dyadique : Par contre, le quotient d'une fraction dyadique par une autre n'est pas, en g\u00E9n\u00E9ral, une fraction dyadique. Ainsi, les fractions dyadiques forment un sous-anneau du corps \u211A des nombres rationnels.Ce sous-anneau est le localis\u00E9 de l'anneau \u2124 des entiers par rapport \u00E0 l'ensemble des puissances de deux. Les nombres surr\u00E9els sont g\u00E9n\u00E9r\u00E9s par un principe de construction it\u00E9rative qui commence en g\u00E9n\u00E9rant toutes les fractions dyadiques finies, puis conduit \u00E0 la cr\u00E9ation de nouvelles et \u00E9tranges sortes de nombres infinis, infinit\u00E9simaux et autres."@fr , "\u0414\u0432\u0456\u0439\u043A\u043E\u0432\u043E-\u0440\u0430\u0446\u0456\u043E\u043D\u0430\u043B\u044C\u043D\u0456 \u0447\u0438\u0441\u043B\u0430 \u2014 \u0440\u0430\u0446\u0456\u043E\u043D\u0430\u043B\u044C\u043D\u0456 \u0447\u0438\u0441\u043B\u0430, \u0437\u043D\u0430\u043C\u0435\u043D\u043D\u0438\u043A \u044F\u043A\u0438\u0445 \u0454 \u0441\u0442\u0435\u043F\u0435\u043D\u0435\u043C \u0434\u0432\u0456\u0439\u043A\u0438. \u0406\u043D\u0430\u043A\u0448\u0435 \u043A\u0430\u0436\u0443\u0447\u0438, \u0447\u0438\u0441\u043B\u0430 \u0432\u0438\u0434\u0443 , \u0434\u0435 \u0446\u0456\u043B\u0435 \u0447\u0438\u0441\u043B\u043E, \u0430 \u043D\u0430\u0442\u0443\u0440\u0430\u043B\u044C\u043D\u0435. \u041D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434, 1/2 \u0456 3/8 \u0434\u0432\u0456\u0439\u043A\u043E\u0432\u043E-\u0440\u0430\u0446\u0456\u043E\u043D\u0430\u043B\u044C\u043D\u0456, \u0430 1/3 \u2014 \u043D\u0456. \u0421\u0430\u043C\u0435 \u0446\u0456 \u0447\u0438\u0441\u043B\u0430 \u043C\u0430\u044E\u0442\u044C \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0435 \u043F\u043E\u0434\u0430\u043D\u043D\u044F \u0432 \u0434\u0432\u0456\u0439\u043A\u043E\u0432\u0456\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u0456 \u0447\u0438\u0441\u043B\u0435\u043D\u043D\u044F."@uk , "\u4E8C\u8FDB\u5206\u6570\uFF0C\u4E5F\u79F0\u4E3A\u4E8C\u8FDB\u6709\u7406\u6570\uFF0C\u662F\u4E00\u79CD\u5206\u6BCD\u662F2\u7684\u5E42\u7684\u5206\u6570\u3002\u53EF\u4EE5\u8868\u793A\u6210\uFF0C\u5176\u4E2D\uFF0C\u662F\u4E00\u4E2A\u6574\u6570\uFF0C\u662F\u4E00\u4E2A\u81EA\u7136\u6570\u3002\u4F8B\u5982\uFF1A\uFF0C\uFF0C\u800C\u5C31\u4E0D\u662F\u3002(\u82F1\u5236\u5355\u4F4D\u4E2D\u5E7F\u6CDB\u91C7\u7528\u4E8C\u8FDB\u5206\u6570\uFF0C\u4F8B\u5982\u82F1\u5BF8\uFF0C\u82F1\u5BF8\uFF0C\u78C5\u3002) \u6240\u6709\u4E8C\u8FDB\u5206\u6570\u7EC4\u6210\u7684\u96C6\u5408\u5728\u5B9E\u6570\u8F74\u4E0A\u662F\u7A20\u5BC6\u7684\uFF1A\u4EFB\u4F55\u5B9E\u6570\u90FD\u53EF\u4EE5\u7528\u5F62\u4E3A\u7684\u4E8C\u8FDB\u5206\u6570\u65E0\u9650\u903C\u8FD1\u3002\u4E0E\u5B9E\u6570\u8F74\u4E0A\u7684\u5176\u5B83\u7A20\u5BC6\u96C6\uFF0C\u4F8B\u5982\u6709\u7406\u6570\u76F8\u6BD4\uFF0C\u4E8C\u8FDB\u5206\u6570\u662F\u76F8\u5BF9\u201C\u5C0F\u201D\u7684\u7A20\u5BC6\u96C6\uFF0C\u8FD9\u5C31\u662F\u4E3A\u4EC0\u4E48\u5B83\u4EEC\u6709\u65F6\u51FA\u73B0\u5728\u8BC1\u660E\u4E2D\uFF08\u4F8B\u5982\u4E4C\u96F7\u677E\u5F15\u7406\uFF09\u3002 \u4EFB\u4F55\u4E24\u4E2A\u4E8C\u8FDB\u5206\u6570\u7684\u548C\u3001\u79EF\uFF0C\u4E0E\u5DEE\u4E5F\u662F\u4E8C\u8FDB\u5206\u6570\uFF1A \u4F46\u662F\uFF0C\u4E24\u4E2A\u4E8C\u8FDB\u5206\u6570\u7684\u5546\u5219\u4E00\u822C\u4E0D\u662F\u4E8C\u8FDB\u5206\u6570\u3002\u56E0\u6B64\uFF0C\u4E8C\u8FDB\u5206\u6570\u5F62\u6210\u4E86\u6709\u7406\u6570\u7684\u4E00\u4E2A\u5B50\u73AF\u3002"@zh , "\u0414\u0432\u043E\u0438\u0447\u043D\u043E-\u0440\u0430\u0446\u0438\u043E\u043D\u0430\u043B\u044C\u043D\u044B\u0435 \u0447\u0438\u0441\u043B\u0430 \u2014 \u0440\u0430\u0446\u0438\u043E\u043D\u0430\u043B\u044C\u043D\u044B\u0435 \u0447\u0438\u0441\u043B\u0430, \u0437\u043D\u0430\u043C\u0435\u043D\u0430\u0442\u0435\u043B\u044C \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u0435\u0442 \u0441\u043E\u0431\u043E\u0439 \u0441\u0442\u0435\u043F\u0435\u043D\u044C \u0434\u0432\u043E\u0439\u043A\u0438. \u0418\u043D\u0430\u0447\u0435 \u0433\u043E\u0432\u043E\u0440\u044F, \u0447\u0438\u0441\u043B\u0430 \u0432\u0438\u0434\u0430 , \u0433\u0434\u0435 \u0446\u0435\u043B\u043E\u0435 \u0447\u0438\u0441\u043B\u043E, \u0430 \u043D\u0430\u0442\u0443\u0440\u0430\u043B\u044C\u043D\u043E\u0435. \u041D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, 1/2 \u0438 3/8 \u0434\u0432\u043E\u0438\u0447\u043D\u043E-\u0440\u0430\u0446\u0438\u043E\u043D\u0430\u043B\u044C\u043D\u044B, \u0430 1/3 \u043D\u0435\u0442. \u0418\u043C\u0435\u043D\u043D\u043E \u044D\u0442\u0438 \u0447\u0438\u0441\u043B\u0430 \u0438\u043C\u0435\u044E\u0442 \u043A\u043E\u043D\u0435\u0447\u043D\u044B\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u044F \u0432 \u0434\u0432\u043E\u0438\u0447\u043D\u043E\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u0435 \u0441\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u044F."@ru . @prefix prov: . dbr:Dyadic_rational prov:wasDerivedFrom . @prefix xsd: . dbr:Dyadic_rational dbo:wikiPageLength "35698"^^xsd:nonNegativeInteger . @prefix wikipedia-en: . dbr:Dyadic_rational foaf:isPrimaryTopicOf wikipedia-en:Dyadic_rational .