. . . "Wohlfundierte Relation"@de . . . . . . . . . "In der Mathematik hei\u00DFt eine auf einer Menge definierte zweistellige Relation wohlfundiert, wenn es keine unendlichen absteigenden Ketten in dieser Relation gibt, d. h., wenn es keine unendliche Folge von Elementen in mit f\u00FCr alle gibt. Insbesondere enth\u00E4lt eine wohlfundierte Relation keine Zyklen."@de . . "\u5728\u6570\u5B66\u4E2D\uFF0C\u985E X \u4E0A\u7684\u4E00\u4E2A\u4E8C\u5143\u5173\u7CFB R \u88AB\u79F0\u4E3A\u662F\u826F\u57FA\u7684\uFF0C\u5F53\u4E14\u4EC5\u5F53\u6240\u6709 X \u7684\u975E\u7A7A\u5B50\u96C6\u90FD\u6709\u4E00\u4E2A R-\u6781\u5C0F\u5143\uFF1B\u5C31\u662F\u8BF4\uFF0C\u5BF9 X \u7684\u6BCF\u4E00\u4E2A\u975E\u7A7A\u5B50\u96C6 S\uFF0C\u5B58\u5728\u4E00\u4E2A S \u4E2D\u7684\u5143\u7D20 m \u4F7F\u5F97\u5BF9\u4E8E\u6240\u6709 S \u4E2D\u7684 s\uFF0C\u4E8C\u5143\u7EC4 (s,m) \u90FD\u4E0D\u5728 R \u4E2D\u3002 \u7B49\u4EF7\u7684\u8BF4\uFF0C\u5047\u5B9A\u67D0\u79CD\u9009\u62E9\u516C\u7406\uFF0C\u4E00\u4E2A\u4E8C\u5143\u5173\u7CFB\u79F0\u4E3A\u662F\u826F\u57FA\u7684\uFF0C\u5F53\u4E14\u4EC5\u5F53\u5B83\u4E0D\u5305\u542B\u53EF\u6570\u7684\u65E0\u7A77\u964D\u94FE\uFF0C\u4E5F\u5C31\u662F\u8BF4\u4E0D\u5B58\u5728 X \u7684\u5143\u7D20\u7684\u65E0\u7A77\u5E8F\u5217 x0, x1, x2, ...\u4F7F\u5F97\u5BF9\u6240\u6709\u7684\u81EA\u7136\u6570 n \u6709\u7740 xn+1 R xn\u3002 \u5728\u5E8F\u7406\u8BBA\u4E2D\uFF0C\u4E00\u4E2A\u504F\u5E8F\u5173\u7CFB\u79F0\u4E3A\u662F\u826F\u57FA\u7684\uFF0C\u5F53\u4E14\u4EC5\u5F53\u5B83\u5BF9\u5E94\u7684\u4E25\u683C\u504F\u5E8F\u662F\u826F\u57FA\u7684\u3002\u5982\u679C\u8FD9\u4E2A\u5E8F\u8FD8\u662F\u5168\u5E8F\uFF0C\u90A3\u4E48\u6B64\u65F6\u79F0\u8FD9\u4E2A\u5E8F\u4E3A\u826F\u5E8F\u3002 \u5728\u96C6\u5408\u8BBA\u4E2D\uFF0C\u4E00\u4E2A\u96C6\u5408 x \u79F0\u4E3A\u662F\u4E00\u4E2A\u826F\u57FA\u96C6\u5408\uFF0C\u5982\u679C\u96C6\u6210\u5458\u5173\u7CFB\u5728 x \u7684\u4F20\u9012\u95ED\u5305\u4E0A\u662F\u826F\u57FA\u7684\u3002\u7B56\u6885\u6D1B-\u5F17\u5170\u514B\u5C14\u96C6\u5408\u8BBA\u4E2D\u7684\u6B63\u5219\u516C\u7406\uFF0C\u5C31\u662F\u65AD\u8A00\u6240\u6709\u7684\u96C6\u5408\u90FD\u662F\u826F\u57FA\u7684\u3002"@zh . "En math\u00E9matiques, une relation bien fond\u00E9e (encore appel\u00E9e relation noeth\u00E9rienne ou relation artinienne) est une relation binaire v\u00E9rifiant l'une des deux conditions suivantes, \u00E9quivalentes d'apr\u00E8s l'axiome du choix d\u00E9pendant (une version faible de l'axiome du choix) : \n* pour toute partie non vide X de E, il existe un \u00E9l\u00E9ment x de X n'ayant aucun R-ant\u00E9c\u00E9dent dans X (un R-ant\u00E9c\u00E9dent de x dans X est un \u00E9l\u00E9ment y de X v\u00E9rifiant yRx) ; \n* condition de cha\u00EEne descendante : il n'existe pas de suite infinie (xn) d'\u00E9l\u00E9ments de E telle qu'on ait xn+1Rxn pour tout n."@fr . . . "Relacja dobrze ufundowana"@pl . . . . . . . "Relacja dobrze ufundowana \u2013 relacja (zwykle cz\u0119\u015Bciowy porz\u0105dek), dla kt\u00F3rej nie istnieje niesko\u0144czony zst\u0119puj\u0105cy ci\u0105g (ka\u017Cdy element tego ci\u0105gu jest w tej relacji z nast\u0119puj\u0105cym bezpo\u015Brednio po nim). Je\u015Bli relacja ma dowolny cykl, to nie jest dobrze ufundowana, poniewa\u017C mo\u017Cna wybiera\u0107 po kolei elementy tego cyklu. Je\u015Bli relacja jest sko\u0144czona i nie ma cykli, to jest dobrze ufundowana. Dla niesko\u0144czonych relacji dobrze ufundowanych cz\u0119sto mo\u017Cna znale\u017A\u0107 dowolnie d\u0142ug\u0105 \u015Bcie\u017Ck\u0119 sko\u0144czon\u0105, na przyk\u0142ad dla porz\u0105dku na mo\u017Cemy wybra\u0107 dowolnie du\u017Cy element pocz\u0105tkowy i ci\u0105g malej\u0105cy o jeden (na przyk\u0142ad 10-elementowy: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0). Relacja, kt\u00F3ra jest dobrze ufundowana i s\u0142abo konfluentna, jest silnie konfluentna. Relacja, kt\u00F3ra jest dobrze ufundowana i spe\u0142nia warunki porz\u0105dku liniowego, jest dobrym porz\u0105dkiem."@pl . . . "Relacja dobrze ufundowana \u2013 relacja (zwykle cz\u0119\u015Bciowy porz\u0105dek), dla kt\u00F3rej nie istnieje niesko\u0144czony zst\u0119puj\u0105cy ci\u0105g (ka\u017Cdy element tego ci\u0105gu jest w tej relacji z nast\u0119puj\u0105cym bezpo\u015Brednio po nim). Je\u015Bli relacja ma dowolny cykl, to nie jest dobrze ufundowana, poniewa\u017C mo\u017Cna wybiera\u0107 po kolei elementy tego cyklu. Je\u015Bli relacja jest sko\u0144czona i nie ma cykli, to jest dobrze ufundowana. Relacja, kt\u00F3ra jest dobrze ufundowana i s\u0142abo konfluentna, jest silnie konfluentna. Relacja, kt\u00F3ra jest dobrze ufundowana i spe\u0142nia warunki porz\u0105dku liniowego, jest dobrym porz\u0105dkiem."@pl . . . "In de wiskunde heet een irreflexieve tweeplaatsige relatie op een klasse welgefundeerd, als elke niet-lege deelverzameling van een element bevat dat geen voorganger heeft, wat in dit verband betekent dat er geen element is waarvoor het paar tot de relatie behoort. Het is dus niet mogelijk dat er een hele keten van elementen is waarvan elk een voorganger heeft, die dus oneindig doorloopt."@nl . . . . "Em matem\u00E1tica, uma rela\u00E7\u00E3o bin\u00E1ria \u00E9 uma rela\u00E7\u00E3o bem-fundada numa classe X, se e somente se, todo subconjunto n\u00E3o vazio de X, tiver um elemento R-minimal; ou seja, para todo subconjunto n\u00E3o vazio S de X, existe um elemento m de S tal que para todo elemento s de S, o par (s,m) n\u00E3o est\u00E1 em R. Em outras palavras, todo subconjunto n\u00E3o vazio de X possui um elemento m tal que para todo s, Desta forma, evitamos situa\u00E7\u00F5es de loop. Formalizando com a l\u00F3gica de predicados, temos: Isto quando tratamos da rela\u00E7\u00E3o de pertin\u00EAncia em teorias de conjuntos bem-fundados. Para uma rela\u00E7\u00E3o R qualquer, equivalentemente podemos denotar, como o descrito no primeiro par\u00E1grafo deste artigo: , onde representa o conjunto (ou classe) das partes de X, caso X o admita (como n\u00E3o \u00E9 o caso de classes pr\u00F3prias). Equivalentemente, assumindo uma fun\u00E7\u00E3o de escolha qualquer, uma rela\u00E7\u00E3o ser\u00E1 bem-fundada se e somente se essa rela\u00E7\u00E3o n\u00E3o contiver cadeia descendente infinitamente enumer\u00E1vel, isto \u00E9, se n\u00E3o existir uma sequ\u00EAncia x0, x1,... de elementos de X, tal que . Na teoria das estruturas ordenadas, uma ordem parcial \u00E9 dita bem-fundada se a correspondente \u00E9 uma rela\u00E7\u00E3o bem-fundada. Se a ordem for uma ordem total, ent\u00E3o ela \u00E9 dita bem-ordenada. Na teoria dos conjuntos, um conjunto \u00DF \u00E9 dito um conjunto bem-fundado se a rela\u00E7\u00E3o de pertin\u00EAncia for bem-fundada no fecho transitivo de \u00DF. O axioma da regularidade, o qual \u00E9 um dos axiomas na teoria dos conjuntos de Zermelo-Fraenkel, afirmando que todos os conjuntos s\u00E3o bem-fundados."@pt . . . . "In mathematics, a binary relation R is called well-founded (or wellfounded) on a class X if every non-empty subset S \u2286 X has a minimal element with respect to R, that is, an element m not related by s R m (for instance, \"s is not smaller than m\") for any s \u2208 S. In other words, a relation is well founded if Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set."@en . "Relaci\u00F3n bien fundada"@es . . . . . . . "Relation bien fond\u00E9e"@fr . . . "In mathematics, a binary relation R is called well-founded (or wellfounded) on a class X if every non-empty subset S \u2286 X has a minimal element with respect to R, that is, an element m not related by s R m (for instance, \"s is not smaller than m\") for any s \u2208 S. In other words, a relation is well founded if Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set. Equivalently, assuming the axiom of dependent choice, a relation is well-founded when it contains no infinite descending chains, which can be proved when there is no infinite sequence x0, x1, x2, ... of elements of X such that xn+1 R xn for every natural number n. In order theory, a partial order is called well-founded if the corresponding strict order is a well-founded relation. If the order is a total order then it is called a well-order. In set theory, a set x is called a well-founded set if the set membership relation is well-founded on the transitive closure of x. The axiom of regularity, which is one of the axioms of Zermelo\u2013Fraenkel set theory, asserts that all sets are well-founded. A relation R is converse well-founded, upwards well-founded or Noetherian on X, if the converse relation R\u22121 is well-founded on X. In this case R is also said to satisfy the ascending chain condition. In the context of rewriting systems, a Noetherian relation is also called terminating."@en . . "\uC9D1\uD569\uB860\uC5D0\uC11C \uC815\uCD08 \uAD00\uACC4(\u6574\u790E\u95DC\u4FC2, \uC601\uC5B4: well-founded relation)\uB294 (\uBB34\uD55C\uD788 \uC7AC\uADC0\uC801\uC774\uC9C0 \uC54A\uC740) \uC9D1\uD569\uC758 \uC6D0\uC18C \uAD00\uACC4\uB85C\uC11C \uB098\uD0C0\uB0BC \uC218 \uC788\uB294 \uC774\uD56D \uAD00\uACC4\uC774\uB2E4. \uC815\uCD08 \uAD00\uACC4\uAC00 \uC8FC\uC5B4\uC9C4 \uC9D1\uD569 \uC704\uC5D0\uC11C\uB294 \uCD08\uD55C \uADC0\uB0A9\uBC95(\u8D85\u9650\u6B78\u7D0D\u6CD5, \uC601\uC5B4: transfinite induction)\uACFC \uCD08\uD55C \uC7AC\uADC0(\u8D85\u9650\u518D\u6B78, \uC601\uC5B4: transfinite recursion)\uB97C \uC0AC\uC6A9\uD560 \uC218 \uC788\uB2E4. \uCD08\uD55C \uADC0\uB0A9\uBC95\uC740 \uBAA8\uB4E0 \uC6D0\uC18C\uAC00 \uC5B4\uB5A4 \uC131\uC9C8\uC744 \uB9CC\uC871\uC2DC\uD0B4\uC744 \uC99D\uBA85\uD560 \uB54C \uC0AC\uC6A9\uD55C\uB2E4. \uCD08\uD55C \uADC0\uB0A9\uBC95\uC5D0 \uB530\uB974\uBA74, \uC5B4\uB5A4 \uC220\uC5B4\uAC00 \uBAA8\uB4E0 \uC6D0\uC18C\uC5D0 \uB300\uD558\uC5EC \uCC38\uC784\uC744 \uBCF4\uC774\uB824\uBA74, \uC8FC\uC5B4\uC9C4 \uC6D0\uC18C \u2018\uC774\uC804\u2019\uC758 \uBAA8\uB4E0 \uC6D0\uC18C\uB4E4\uC5D0 \uB300\uD558\uC5EC \uCC38\uC784\uC744 \uAC00\uC815\uD55C \uCC44\uB85C, \uADF8 \uC8FC\uC5B4\uC9C4 \uC6D0\uC18C\uC5D0 \uB300\uD558\uC5EC \uCC38\uC784\uC744 \uBCF4\uC774\uBA74 \uCDA9\uBD84\uD558\uB2E4. \uC774\uB294 \uC790\uC5F0\uC218\uC5D0 \uB300\uD55C \uC218\uD559\uC801 \uADC0\uB0A9\uBC95\uC744 \uC77C\uBC18\uD654\uD55C\uB2E4. \uCD08\uD55C \uC7AC\uADC0\uB294 \uC815\uCD08 \uAD00\uACC4\uAC00 \uC8FC\uC5B4\uC9C4 \uC9D1\uD569\uC744 \uC815\uC758\uC5ED\uC73C\uB85C \uD558\uB294 \uD568\uC218\uB97C \uC815\uC758\uD558\uB294 \uBC29\uBC95\uC774\uB2E4. \uCD08\uD55C \uC7AC\uADC0\uC5D0 \uB530\uB974\uBA74, \uC8FC\uC5B4\uC9C4 \uC6D0\uC18C\uC758 \uD568\uC22B\uAC12\uC744 \uADF8 \u2018\uC774\uC804\u2019\uC758 \uC6D0\uC18C\uB4E4\uC758 \uD568\uC22B\uAC12\uB4E4\uB85C\uBD80\uD130 \uACB0\uC815\uD558\uB294 \uBC29\uBC95(\uC5D0\uC11C\uC758 \uD568\uC218 )\uC774 \uC815\uD574\uC84C\uC744 \uB54C, \uBAA8\uB4E0 \uC6D0\uC18C\uC5D0 \uB300\uD55C \uD568\uC22B\uAC12\uC740 \uC720\uC77C\uD558\uAC8C \uACB0\uC815\uB41C\uB2E4."@ko . . . . . . . . "In der Mathematik hei\u00DFt eine auf einer Menge definierte zweistellige Relation wohlfundiert, wenn es keine unendlichen absteigenden Ketten in dieser Relation gibt, d. h., wenn es keine unendliche Folge von Elementen in mit f\u00FCr alle gibt. Insbesondere enth\u00E4lt eine wohlfundierte Relation keine Zyklen."@de . "Relazione ben fondata"@it . "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456, \u0431\u0456\u043D\u0430\u0440\u043D\u0435 \u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u044F R \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0444\u0443\u043D\u0434\u043E\u0432\u0430\u043D\u0438\u043C \u043D\u0430 \u043A\u043B\u0430\u0441\u0456 X \u044F\u043A\u0449\u043E \u043D\u0435\u043F\u043E\u0440\u043E\u0436\u043D\u044F \u043C\u043D\u043E\u0436\u0438\u043D\u0430 S \u2286 X \u043C\u0430\u0454 \u043C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u0438\u0439 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 \u043F\u043E \u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u044E \u0434\u043E R, \u0442\u043E\u0431\u0442\u043E, \u0442\u0430\u043A\u0438\u0439 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 m, \u0434\u043B\u044F \u044F\u043A\u043E\u0433\u043E \u043D\u0435 \u0456\u0441\u043D\u0443\u0454 s R m (\u0434\u043B\u044F \u0432\u0441\u0456\u0445 s \u2208 S. \u0424\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E:"@uk . "En matem\u00E0tiques, una relaci\u00F3 binaria R est\u00E0 ben fonamentada en una classe X si, i nom\u00E9s si, cada subconjunt no buit d'X t\u00E9 un element minimal respecte de R. Aix\u00F2 \u00E9s, per cada subconjunt no buit S de X, existeix un element m de S tal que per cada element s de S, la parella (s,m) no pertany a R: Equivalentment, assumint una elecci\u00F3, una relaci\u00F3 est\u00E0 ben fonamentada si, i nom\u00E9s si, no cont\u00E9 cap : aix\u00F2 \u00E9s, no existeix cap seq\u00FC\u00E8ncia infinita x0, x1, x\u2082, ... d'elements de X tal que xn+1 R xn per cada nombre natural n."@ca . . . . . . "\u826F\u57FA\u5173\u7CFB"@zh . . . . "En teor\u00EDa de conjuntos, una relaci\u00F3n bien fundada sobre una clase X es una relaci\u00F3n binaria R sobre X tal que todo subconjunto no vac\u00EDo de X tiene un elemento R-m\u00EDnimo; esto es: Equivalentemente, si asumimos el axioma de elecci\u00F3n, una relaci\u00F3n es bien fundada si y s\u00F3lo si X no contiene cadenas descendientes infinitas numerables: esto es, no hay secuencia infinita x0, x1, x2, ... de elementos de X tal que xn+1R xn para todo n\u00FAmero natural n.\u200B"@es . "319712"^^ . "En teor\u00EDa de conjuntos, una relaci\u00F3n bien fundada sobre una clase X es una relaci\u00F3n binaria R sobre X tal que todo subconjunto no vac\u00EDo de X tiene un elemento R-m\u00EDnimo; esto es: Equivalentemente, si asumimos el axioma de elecci\u00F3n, una relaci\u00F3n es bien fundada si y s\u00F3lo si X no contiene cadenas descendientes infinitas numerables: esto es, no hay secuencia infinita x0, x1, x2, ... de elementos de X tal que xn+1R xn para todo n\u00FAmero natural n.\u200B \n* En la teor\u00EDa del orden, un orden parcial es llamado bien fundado si el correspondiente es una relaci\u00F3n bien fundada. Si el orden bien fundado es un orden total entonces es un buen orden. \n* Un conjunto X se dice regular si la relaci\u00F3n de pertenencia \u2208 est\u00E1 bien fundada en la clausura transitiva de X, ct X. Esto implica que no existen dentro de X conjuntos del tipo A={A}={{A}}=... En teor\u00EDa axiom\u00E1tica de conjuntos, el axioma de regularidad afirma que todos los conjuntos son regulares."@es . . . "Fundovan\u00E1 relace"@cs . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u4E8C\u9805\u95A2\u4FC2\u304C\u6574\u790E\uFF08\u305B\u3044\u305D\u3001\u82F1: well-founded\uFF09\u3067\u3042\u308B\u3068\u306F\u3001\u771F\u306E\u7121\u9650\u3092\u3082\u305F\u306A\u3044\u3053\u3068\u3067\u3042\u308B\u3002"@ja . . "\u0424\u0443\u043D\u0434\u043E\u0432\u0430\u043D\u0435 \u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u044F"@uk . . . . . "Fundovan\u00E1 relace je matematick\u00FD pojem z oboru teorie mno\u017Ein, kter\u00FD popisuje druh relace podobn\u00FD dobr\u00E9mu uspo\u0159\u00E1d\u00E1n\u00ED."@cs . . "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456, \u0431\u0456\u043D\u0430\u0440\u043D\u0435 \u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u044F R \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0444\u0443\u043D\u0434\u043E\u0432\u0430\u043D\u0438\u043C \u043D\u0430 \u043A\u043B\u0430\u0441\u0456 X \u044F\u043A\u0449\u043E \u043D\u0435\u043F\u043E\u0440\u043E\u0436\u043D\u044F \u043C\u043D\u043E\u0436\u0438\u043D\u0430 S \u2286 X \u043C\u0430\u0454 \u043C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u0438\u0439 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 \u043F\u043E \u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u044E \u0434\u043E R, \u0442\u043E\u0431\u0442\u043E, \u0442\u0430\u043A\u0438\u0439 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 m, \u0434\u043B\u044F \u044F\u043A\u043E\u0433\u043E \u043D\u0435 \u0456\u0441\u043D\u0443\u0454 s R m (\u0434\u043B\u044F \u0432\u0441\u0456\u0445 s \u2208 S. \u0424\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E:"@uk . . . "Relaci\u00F3 ben fonamentada"@ca . "Fundovan\u00E1 relace je matematick\u00FD pojem z oboru teorie mno\u017Ein, kter\u00FD popisuje druh relace podobn\u00FD dobr\u00E9mu uspo\u0159\u00E1d\u00E1n\u00ED."@cs . "En math\u00E9matiques, une relation bien fond\u00E9e (encore appel\u00E9e relation noeth\u00E9rienne ou relation artinienne) est une relation binaire v\u00E9rifiant l'une des deux conditions suivantes, \u00E9quivalentes d'apr\u00E8s l'axiome du choix d\u00E9pendant (une version faible de l'axiome du choix) : \n* pour toute partie non vide X de E, il existe un \u00E9l\u00E9ment x de X n'ayant aucun R-ant\u00E9c\u00E9dent dans X (un R-ant\u00E9c\u00E9dent de x dans X est un \u00E9l\u00E9ment y de X v\u00E9rifiant yRx) ; \n* condition de cha\u00EEne descendante : il n'existe pas de suite infinie (xn) d'\u00E9l\u00E9ments de E telle qu'on ait xn+1Rxn pour tout n. Un ordre bien fond\u00E9 (encore appel\u00E9 ordre noeth\u00E9rien ou ordre artinien) est une relation d'ordre dont l'ordre strict associ\u00E9 est une relation bien fond\u00E9e. Toute relation bien fond\u00E9e est strictement acyclique, c'est-\u00E0-dire que sa cl\u00F4ture transitive est un ordre strict. Une relation R est bien fond\u00E9e si sa cl\u00F4ture transitive l'est, ou encore si R est antir\u00E9flexive et si sa cl\u00F4ture r\u00E9flexive transitive est un ordre bien fond\u00E9."@fr . "Welgefundeerde relatie"@nl . . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u4E8C\u9805\u95A2\u4FC2\u304C\u6574\u790E\uFF08\u305B\u3044\u305D\u3001\u82F1: well-founded\uFF09\u3067\u3042\u308B\u3068\u306F\u3001\u771F\u306E\u7121\u9650\u3092\u3082\u305F\u306A\u3044\u3053\u3068\u3067\u3042\u308B\u3002"@ja . . . "\u5728\u6570\u5B66\u4E2D\uFF0C\u985E X \u4E0A\u7684\u4E00\u4E2A\u4E8C\u5143\u5173\u7CFB R \u88AB\u79F0\u4E3A\u662F\u826F\u57FA\u7684\uFF0C\u5F53\u4E14\u4EC5\u5F53\u6240\u6709 X \u7684\u975E\u7A7A\u5B50\u96C6\u90FD\u6709\u4E00\u4E2A R-\u6781\u5C0F\u5143\uFF1B\u5C31\u662F\u8BF4\uFF0C\u5BF9 X \u7684\u6BCF\u4E00\u4E2A\u975E\u7A7A\u5B50\u96C6 S\uFF0C\u5B58\u5728\u4E00\u4E2A S \u4E2D\u7684\u5143\u7D20 m \u4F7F\u5F97\u5BF9\u4E8E\u6240\u6709 S \u4E2D\u7684 s\uFF0C\u4E8C\u5143\u7EC4 (s,m) \u90FD\u4E0D\u5728 R \u4E2D\u3002 \u7B49\u4EF7\u7684\u8BF4\uFF0C\u5047\u5B9A\u67D0\u79CD\u9009\u62E9\u516C\u7406\uFF0C\u4E00\u4E2A\u4E8C\u5143\u5173\u7CFB\u79F0\u4E3A\u662F\u826F\u57FA\u7684\uFF0C\u5F53\u4E14\u4EC5\u5F53\u5B83\u4E0D\u5305\u542B\u53EF\u6570\u7684\u65E0\u7A77\u964D\u94FE\uFF0C\u4E5F\u5C31\u662F\u8BF4\u4E0D\u5B58\u5728 X \u7684\u5143\u7D20\u7684\u65E0\u7A77\u5E8F\u5217 x0, x1, x2, ...\u4F7F\u5F97\u5BF9\u6240\u6709\u7684\u81EA\u7136\u6570 n \u6709\u7740 xn+1 R xn\u3002 \u5728\u5E8F\u7406\u8BBA\u4E2D\uFF0C\u4E00\u4E2A\u504F\u5E8F\u5173\u7CFB\u79F0\u4E3A\u662F\u826F\u57FA\u7684\uFF0C\u5F53\u4E14\u4EC5\u5F53\u5B83\u5BF9\u5E94\u7684\u4E25\u683C\u504F\u5E8F\u662F\u826F\u57FA\u7684\u3002\u5982\u679C\u8FD9\u4E2A\u5E8F\u8FD8\u662F\u5168\u5E8F\uFF0C\u90A3\u4E48\u6B64\u65F6\u79F0\u8FD9\u4E2A\u5E8F\u4E3A\u826F\u5E8F\u3002 \u5728\u96C6\u5408\u8BBA\u4E2D\uFF0C\u4E00\u4E2A\u96C6\u5408 x \u79F0\u4E3A\u662F\u4E00\u4E2A\u826F\u57FA\u96C6\u5408\uFF0C\u5982\u679C\u96C6\u6210\u5458\u5173\u7CFB\u5728 x \u7684\u4F20\u9012\u95ED\u5305\u4E0A\u662F\u826F\u57FA\u7684\u3002\u7B56\u6885\u6D1B-\u5F17\u5170\u514B\u5C14\u96C6\u5408\u8BBA\u4E2D\u7684\u6B63\u5219\u516C\u7406\uFF0C\u5C31\u662F\u65AD\u8A00\u6240\u6709\u7684\u96C6\u5408\u90FD\u662F\u826F\u57FA\u7684\u3002"@zh . "Well-founded relation"@en . "In de wiskunde heet een irreflexieve tweeplaatsige relatie op een klasse welgefundeerd, als elke niet-lege deelverzameling van een element bevat dat geen voorganger heeft, wat in dit verband betekent dat er geen element is waarvoor het paar tot de relatie behoort. Het is dus niet mogelijk dat er een hele keten van elementen is waarvan elk een voorganger heeft, die dus oneindig doorloopt."@nl . . . "1108316869"^^ . . . . . . . . "Em matem\u00E1tica, uma rela\u00E7\u00E3o bin\u00E1ria \u00E9 uma rela\u00E7\u00E3o bem-fundada numa classe X, se e somente se, todo subconjunto n\u00E3o vazio de X, tiver um elemento R-minimal; ou seja, para todo subconjunto n\u00E3o vazio S de X, existe um elemento m de S tal que para todo elemento s de S, o par (s,m) n\u00E3o est\u00E1 em R. Em outras palavras, todo subconjunto n\u00E3o vazio de X possui um elemento m tal que para todo s, Desta forma, evitamos situa\u00E7\u00F5es de loop. Formalizando com a l\u00F3gica de predicados, temos: Isto quando tratamos da rela\u00E7\u00E3o de pertin\u00EAncia em teorias de conjuntos bem-fundados."@pt . . "\uC815\uCD08 \uAD00\uACC4"@ko . "\u6574\u790E\u95A2\u4FC2"@ja . . . . "\uC9D1\uD569\uB860\uC5D0\uC11C \uC815\uCD08 \uAD00\uACC4(\u6574\u790E\u95DC\u4FC2, \uC601\uC5B4: well-founded relation)\uB294 (\uBB34\uD55C\uD788 \uC7AC\uADC0\uC801\uC774\uC9C0 \uC54A\uC740) \uC9D1\uD569\uC758 \uC6D0\uC18C \uAD00\uACC4\uB85C\uC11C \uB098\uD0C0\uB0BC \uC218 \uC788\uB294 \uC774\uD56D \uAD00\uACC4\uC774\uB2E4. \uC815\uCD08 \uAD00\uACC4\uAC00 \uC8FC\uC5B4\uC9C4 \uC9D1\uD569 \uC704\uC5D0\uC11C\uB294 \uCD08\uD55C \uADC0\uB0A9\uBC95(\u8D85\u9650\u6B78\u7D0D\u6CD5, \uC601\uC5B4: transfinite induction)\uACFC \uCD08\uD55C \uC7AC\uADC0(\u8D85\u9650\u518D\u6B78, \uC601\uC5B4: transfinite recursion)\uB97C \uC0AC\uC6A9\uD560 \uC218 \uC788\uB2E4. \uCD08\uD55C \uADC0\uB0A9\uBC95\uC740 \uBAA8\uB4E0 \uC6D0\uC18C\uAC00 \uC5B4\uB5A4 \uC131\uC9C8\uC744 \uB9CC\uC871\uC2DC\uD0B4\uC744 \uC99D\uBA85\uD560 \uB54C \uC0AC\uC6A9\uD55C\uB2E4. \uCD08\uD55C \uADC0\uB0A9\uBC95\uC5D0 \uB530\uB974\uBA74, \uC5B4\uB5A4 \uC220\uC5B4\uAC00 \uBAA8\uB4E0 \uC6D0\uC18C\uC5D0 \uB300\uD558\uC5EC \uCC38\uC784\uC744 \uBCF4\uC774\uB824\uBA74, \uC8FC\uC5B4\uC9C4 \uC6D0\uC18C \u2018\uC774\uC804\u2019\uC758 \uBAA8\uB4E0 \uC6D0\uC18C\uB4E4\uC5D0 \uB300\uD558\uC5EC \uCC38\uC784\uC744 \uAC00\uC815\uD55C \uCC44\uB85C, \uADF8 \uC8FC\uC5B4\uC9C4 \uC6D0\uC18C\uC5D0 \uB300\uD558\uC5EC \uCC38\uC784\uC744 \uBCF4\uC774\uBA74 \uCDA9\uBD84\uD558\uB2E4. \uC774\uB294 \uC790\uC5F0\uC218\uC5D0 \uB300\uD55C \uC218\uD559\uC801 \uADC0\uB0A9\uBC95\uC744 \uC77C\uBC18\uD654\uD55C\uB2E4. \uCD08\uD55C \uC7AC\uADC0\uB294 \uC815\uCD08 \uAD00\uACC4\uAC00 \uC8FC\uC5B4\uC9C4 \uC9D1\uD569\uC744 \uC815\uC758\uC5ED\uC73C\uB85C \uD558\uB294 \uD568\uC218\uB97C \uC815\uC758\uD558\uB294 \uBC29\uBC95\uC774\uB2E4. \uCD08\uD55C \uC7AC\uADC0\uC5D0 \uB530\uB974\uBA74, \uC8FC\uC5B4\uC9C4 \uC6D0\uC18C\uC758 \uD568\uC22B\uAC12\uC744 \uADF8 \u2018\uC774\uC804\u2019\uC758 \uC6D0\uC18C\uB4E4\uC758 \uD568\uC22B\uAC12\uB4E4\uB85C\uBD80\uD130 \uACB0\uC815\uD558\uB294 \uBC29\uBC95(\uC5D0\uC11C\uC758 \uD568\uC218 )\uC774 \uC815\uD574\uC84C\uC744 \uB54C, \uBAA8\uB4E0 \uC6D0\uC18C\uC5D0 \uB300\uD55C \uD568\uC22B\uAC12\uC740 \uC720\uC77C\uD558\uAC8C \uACB0\uC815\uB41C\uB2E4."@ko . . "Rela\u00E7\u00E3o bem-fundada"@pt . . . . "En matem\u00E0tiques, una relaci\u00F3 binaria R est\u00E0 ben fonamentada en una classe X si, i nom\u00E9s si, cada subconjunt no buit d'X t\u00E9 un element minimal respecte de R. Aix\u00F2 \u00E9s, per cada subconjunt no buit S de X, existeix un element m de S tal que per cada element s de S, la parella (s,m) no pertany a R: Equivalentment, assumint una elecci\u00F3, una relaci\u00F3 est\u00E0 ben fonamentada si, i nom\u00E9s si, no cont\u00E9 cap : aix\u00F2 \u00E9s, no existeix cap seq\u00FC\u00E8ncia infinita x0, x1, x\u2082, ... d'elements de X tal que xn+1 R xn per cada nombre natural n. En Teoria de l'ordre, un conjunt parcialment ordenat est\u00E0 ben fonamentada si l' corresponent \u00E9s una relaci\u00F3 ben fonamentada. Si l'orde \u00E9s un ordre total llavors s'anomena . En Teoria de conjunts, un conjunt x s'anomena conjunt ben fonamentat si la relaci\u00F3 de ser membre est\u00E0 ben formada per la de x. En aquest cas R satisf\u00E0 tamb\u00E9 la ."@ca . "9285"^^ .