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Enumeración Enumeration 列举法 (集合论) Enumerazione (matematica) 数え上げ Enumeração
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Em matemática e ciência da computação teórica, a enumeração é a repetiçao de diversas palavras seguidas de virgula. Enumerazione è il nome dato ad un generico campo della matematica che si occupa di contare gli oggetti. Il conteggio viene astratto il più possibile dagli oggetti in questione, in modo da ottenere tecniche di conteggio generiche che non fanno affidamento su proprietà specifiche di certi gruppi di oggetti. Tra i settori dell'enumerazione vi sono l' e l'. En matemática e informática teórica, la definición más amplia y más abstracta de una enumeración de un conjunto es un listado exacto de todos sus elementos (tal vez con repetición). Las restricciones impuestas al tipo de listado usado depende de la rama de la matemática y el contexto en el cual se trabaja. Formalmente, en matemáticas, una enumeración de un conjunto A es una aplicación biyectiva . Un conjunto enumerable es un conjunto para el cual existe una enumeración (de hecho si existe al menos una enumeración existirán infinitas enumeraciones). 数え上げ(かぞえあげ)は、数学においては、ある集合に対し、その集合から自然数全体の成す集合への単射を定義することである。また、そのような単射が少なくとも1つ存在するならば数え上げ可能であると言い、1つも存在しないならば数え上げ不可能であると言う。 列举法是集合论(或者类的理论)中表示集合(或类)的一种方法。 如果已知集合(或类)的每一个元素,而且元素个数“相当有限”,我们可以通过“列举”其所有元素的方法来表示这个,如:{1,2,3}、{a}、{A,B,C,D,E}等。一对花括号“{ }”是集合(或类)表示法的特征符号。 如果集合(或类)的元素有“很多”甚至“无限多”以至于很难或无法将其所有元素一一列出,但其元素又具有很明显的“规律”,可以用“…”略过规律性比较明显的大量元素,如用{1,2,…,100}表示其元素为从1到100的所有自然数、{A,B,…,Z}表示所有的大写英文字母、{3,4,5,…}表示从3开始的所有自然数,等等。 列举法的实质是给出了集合(或类)的外延,因此又称为外延法。如果在列举法中列出了集合(或类)的所有元素,此时称为完全列举法,否则就称为部分列举法。 An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem.
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Enumerazione è il nome dato ad un generico campo della matematica che si occupa di contare gli oggetti. Il conteggio viene astratto il più possibile dagli oggetti in questione, in modo da ottenere tecniche di conteggio generiche che non fanno affidamento su proprietà specifiche di certi gruppi di oggetti. Tra i settori dell'enumerazione vi sono l' e l'. An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem. Some sets can be enumerated by means of a natural ordering (such as 1, 2, 3, 4, ... for the set of positive integers), but in other cases it may be necessary to impose a (perhaps arbitrary) ordering. In some contexts, such as enumerative combinatorics, the term enumeration is used more in the sense of counting – with emphasis on determination of the number of elements that a set contains, rather than the production of an explicit listing of those elements. 数え上げ(かぞえあげ)は、数学においては、ある集合に対し、その集合から自然数全体の成す集合への単射を定義することである。また、そのような単射が少なくとも1つ存在するならば数え上げ可能であると言い、1つも存在しないならば数え上げ不可能であると言う。 En matemática e informática teórica, la definición más amplia y más abstracta de una enumeración de un conjunto es un listado exacto de todos sus elementos (tal vez con repetición). Las restricciones impuestas al tipo de listado usado depende de la rama de la matemática y el contexto en el cual se trabaja. Específicamente, la noción de enumeración contiene dos tipos diferentes de listado: uno donde hay una ordenación natural y uno donde la ordenación es más difusa. Estas dos clases diferentes de enumeración corresponden al procedimiento para listar todos los miembros de un conjunto en una sucesión definida, o un conteo de elementos de una clase. Mientras estas dos clases de enumeración usualmente se superponen en la situaciones más naturales, pueden tener significados muy distintos en ciertos contextos. Formalmente, en matemáticas, una enumeración de un conjunto A es una aplicación biyectiva . Un conjunto enumerable es un conjunto para el cual existe una enumeración (de hecho si existe al menos una enumeración existirán infinitas enumeraciones). 列举法是集合论(或者类的理论)中表示集合(或类)的一种方法。 如果已知集合(或类)的每一个元素,而且元素个数“相当有限”,我们可以通过“列举”其所有元素的方法来表示这个,如:{1,2,3}、{a}、{A,B,C,D,E}等。一对花括号“{ }”是集合(或类)表示法的特征符号。 如果集合(或类)的元素有“很多”甚至“无限多”以至于很难或无法将其所有元素一一列出,但其元素又具有很明显的“规律”,可以用“…”略过规律性比较明显的大量元素,如用{1,2,…,100}表示其元素为从1到100的所有自然数、{A,B,…,Z}表示所有的大写英文字母、{3,4,5,…}表示从3开始的所有自然数,等等。 列举法的实质是给出了集合(或类)的外延,因此又称为外延法。如果在列举法中列出了集合(或类)的所有元素,此时称为完全列举法,否则就称为部分列举法。 Em matemática e ciência da computação teórica, a enumeração é a repetiçao de diversas palavras seguidas de virgula.
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