@prefix dbpprop: .
@prefix dbpedia: .
dbpedia:Inductive_definition dbpprop:redirect dbpedia:Recursive_definition .
@prefix owl: .
dbpedia:Recursive_definition owl:sameAs .
@prefix foaf: .
@prefix ns4: .
dbpedia:Recursive_definition foaf:page ns4:Recursive_definition .
@prefix rdfs: .
dbpedia:Recursive_definition rdfs:label "Definizione ricorsiva"@it ,
"Recursive definition"@en ,
"\u0420\u0435\u043A\u0443\u0440\u0441\u0438\u0432\u043D\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435"@ru ,
"\u518D\u5E30\u7684\u5B9A\u7FA9"@ja .
@prefix dbpedia-owl: .
dbpedia:Recursive_definition dbpedia-owl:thumbnail ;
dbpprop:abstract "In mathematical logic and computer science, a recursive definition (or inductive definition) is used to define an object in terms of itself . A recursive definition of a function defines values of the functions for some inputs in terms of the values of the same function for other inputs. For example, the factorial function n! is defined by the rules (n+1)! = (n+1)· n!. This definition is valid because, for all n, the recursion eventually reaches the base case of 0. Thus the definition is well-founded. An inductive definition of a set describes the elements in a set in terms of other elements in the set. For example, one definition of the set N of natural numbers is: 0 is in N. If an element n is in N then n+1 is in N. N is the smallest set such satisfying (1) and (2). There are many sets that satisfy (1) and (2); clause (3) makes the definition precise by choosing the smallest such set as N. Properties of recursively defined functions and sets can often be proved by an induction principle the follows the recursive definition. For example, the definition of the natural numbers presented here directly implies the principle of mathematical induction for natural numbers: if a property holds of the natural number 0, and the property holds of n+1 whenever it holds of n, then the property holds of all natural numbers ."@en ,
"\u518D\u5E30\u7684\u5B9A\u7FA9\uFF08Recursive Definition\uFF09\u306F\u3001\u518D\u5E30\u7684\u306A\u5B9A\u7FA9\u3001\u3059\u306A\u308F\u3061\u3001\u3042\u308B\u3082\u306E\u3092\u5B9A\u7FA9\u3059\u308B\u306B\u3042\u305F\u3063\u3066\u305D\u308C\u81EA\u8EAB\u3092\u5B9A\u7FA9\u306B\u542B\u3080\u3082\u306E\u3092\u8A00\u3046\u3002\u7121\u9650\u56DE\u5E30\u3092\u907F\u3051\u308B\u305F\u3081\u3001\u5B9A\u7FA9\u306B\u542B\u307E\u308C\u308B\u300C\u305D\u308C\u81EA\u8EAB\u300D\u306F\u3088\u304F\u5B9A\u7FA9\u3055\u308C\u3066\u3044\u306A\u3051\u308C\u3070\u306A\u3089\u306A\u3044\u3002\u540C\u7FA9\u8A9E\u3068\u3057\u3066\u5E30\u7D0D\u7684\u5B9A\u7FA9\uFF08Inductive Definition\uFF09\u304C\u3042\u308B\u3002"@ja ,
"In matematica una definizione ricorsiva di un insieme A si ha quando per definire A vengono elencati degli elementi di A e delle regole per costruire nuovi elementi di A a partire da elementi di A. Ad esempio l'insieme P dei numeri pari pu\u00F2 essere definito ricorsivamente dicendo: 2 appartiene a P se un numero n appartiene a P allora anche n+2 appartiene a P Una definizione ricorsiva di una funzione f definita sui numeri naturali si ha quando f viene definita elencando i valori che assume su 0 e dando una regola per calcolare il valore della funzione su n a partire dal valore che assume su n-1. Anche in ambiente informatico l'uso della definizione ricorsiva \u00E8 piuttosto comune, soprattutto sotto forma di acronimo ricorsivo: un esempio molto noto \u00E8 GNU = GNU's Not Unix dove si pu\u00F2 notare come il nome \u00E8 la parte in un certo senso meno importante della definizione stessa. Infine, l'induzione matematica pu\u00F2 portare a una specie di definizione ricorsiva, dove per\u00F2 c'\u00E8 un caso speciale al quale tutti gli altri prima o poi devono giungere e che quindi fa terminare la ricorsione. Ad esempio, per calcolare il fattoriale di un numero positivo n, si pu\u00F2 dire il fattoriale di 1 \u00E8 1; il fattoriale di n \u00E8 n volte il fattoriale di (n-1), se n \u00E8 maggiore di 1."@it ,
"\u0420\u0435\u043A\u0443\u0440\u0441\u0438\u0432\u043D\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u0438\u043B\u0438 \u0438\u043D\u0434\u0443\u043A\u0442\u0438\u0432\u043D\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u044F\u0435\u0442 \u0441\u0443\u0449\u043D\u043E\u0441\u0442\u044C \u0432 \u0442\u0435\u0440\u043C\u0438\u043D\u0430\u0445 \u0435\u0451 \u0441\u0430\u043C\u043E\u0439, \u0445\u043E\u0442\u044F \u0438 \u043F\u043E\u043B\u0435\u0437\u043D\u044B\u043C \u0441\u043F\u043E\u0441\u043E\u0431\u043E\u043C. \u0414\u043B\u044F \u0442\u043E\u0433\u043E, \u0447\u0442\u043E\u0431\u044B \u044D\u0442\u043E \u0431\u044B\u043B\u043E \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E, \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u0432 \u043B\u044E\u0431\u043E\u043C \u0434\u0430\u043D\u043D\u043E\u043C \u0441\u043B\u0443\u0447\u0430\u0435 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\u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435: \u0441\u043C. \u0420\u0435\u043A\u0443\u0440\u0441\u0438\u0432\u043D\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435\" \u043D\u0435\u043A\u043E\u0440\u0440\u0435\u043A\u0442\u043D\u0430: \u043D\u0430 \u0441\u0430\u043C\u043E\u043C \u0434\u0435\u043B\u0435 \u044D\u0442\u043E \u0446\u0438\u043A\u043B\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435."@ru ;
rdfs:comment "\u518D\u5E30\u7684\u5B9A\u7FA9\uFF08Recursive Definition\uFF09\u306F\u3001\u518D\u5E30\u7684\u306A\u5B9A\u7FA9\u3001\u3059\u306A\u308F\u3061\u3001\u3042\u308B\u3082\u306E\u3092\u5B9A\u7FA9\u3059\u308B\u306B\u3042\u305F\u3063\u3066\u305D\u308C\u81EA\u8EAB\u3092\u5B9A\u7FA9\u306B\u542B\u3080\u3082\u306E\u3092\u8A00\u3046\u3002\u7121\u9650\u56DE\u5E30\u3092\u907F\u3051\u308B\u305F\u3081\u3001\u5B9A\u7FA9\u306B\u542B\u307E\u308C\u308B\u300C\u305D\u308C\u81EA\u8EAB\u300D\u306F\u3088\u304F\u5B9A\u7FA9\u3055\u308C\u3066\u3044\u306A\u3051\u308C\u3070\u306A\u3089\u306A\u3044\u3002\u540C\u7FA9\u8A9E\u3068\u3057\u3066\u5E30\u7D0D\u7684\u5B9A\u7FA9\uFF08Inductive Definition\uFF09\u304C\u3042\u308B\u3002"@ja ,
"In matematica una definizione ricorsiva di un insieme A si ha quando per definire A vengono elencati degli elementi di A e delle regole per costruire nuovi elementi di A a partire da elementi di A."@it ,
"\u0420\u0435\u043A\u0443\u0440\u0441\u0438\u0432\u043D\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u0438\u043B\u0438 \u0438\u043D\u0434\u0443\u043A\u0442\u0438\u0432\u043D\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u044F\u0435\u0442 \u0441\u0443\u0449\u043D\u043E\u0441\u0442\u044C \u0432 \u0442\u0435\u0440\u043C\u0438\u043D\u0430\u0445 \u0435\u0451 \u0441\u0430\u043C\u043E\u0439, \u0445\u043E\u0442\u044F \u0438 \u043F\u043E\u043B\u0435\u0437\u043D\u044B\u043C \u0441\u043F\u043E\u0441\u043E\u0431\u043E\u043C. \u0414\u043B\u044F \u0442\u043E\u0433\u043E, \u0447\u0442\u043E\u0431\u044B \u044D\u0442\u043E \u0431\u044B\u043B\u043E \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E, \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u0432 \u043B\u044E\u0431\u043E\u043C \u0434\u0430\u043D\u043D\u043E\u043C \u0441\u043B\u0443\u0447\u0430\u0435 \u0434\u043E\u043B\u0436\u043D\u043E \u0431\u044B\u0442\u044C \u0445\u043E\u0440\u043E\u0448\u043E-\u043E\u0441\u043D\u043E\u0432\u0430\u043D\u043D\u044B\u043C, \u0438\u0437\u0431\u0435\u0433\u0430\u044F \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438."@ru ,
"In mathematical logic and computer science, a recursive definition (or inductive definition) is used to define an object in terms of itself . A recursive definition of a function defines values of the functions for some inputs in terms of the values of the same function for other inputs. For example, the factorial function n! is defined by the rules (n+1)! = (n+1)· n!. This definition is valid because, for all n, the recursion eventually reaches the base case of 0."@en ;
foaf:depiction .
@prefix skos: .
@prefix ns8: .
dbpedia:Recursive_definition skos:subject ns8:Theoretical_computer_science ,
ns8:Definition ,
ns8:Mathematical_logic .
@prefix ns9: .
dbpedia:Recursive_definition dbpprop:hasPhotoCollection ns9:Recursive_definition .
dbpedia:Recursively_define dbpprop:redirect dbpedia:Recursive_definition .