In set theory, the complement of a set, often denoted by (or ), are the elements not in. When all sets under consideration are considered to be subsets of a given set, the absolute complement of is the set of elements in that are not in. The relative complement of with respect to a set, also termed the set difference of and, written is the set of elements in that are not in. Absolute complement Definition If is a set, then the absolute complement of (or simply the complement of ) is the set of elements not in (within a larger set that is implicitly defined). In other words, let be a set that contains all the elements under study; if there is no need to mention, either because it has been previously specified, or it is obvious and unique, then the absolute complement of is the relative complement of in : Or formally: The absolute complement of is usually denoted by Other notations include Examples Assume that the universe is the set of integers. If is the set of odd numbers, then the complement of is the set of even numbers. If is the set of multiples of 3, then the complement of is the
En teoría de conjuntos, el complemento relativo de con respecto a un conjunto, también llamado la diferencia de conjunto de y, escrito es el conjunto de elementos en que no están en. Definición de complemento absoluto Si es un conjunto, entonces el complemento absoluto de (o simplemente el complemento de ) es el conjunto de elementos no en (dentro de un conjunto más grande que está implícitamente definido). En otras palabras, deje que sea un conjunto que contenga todos los elementos bajo estudio; si no hay necesidad de mencionar, ya sea porque ha sido previamente especificado, o es obvio y único, entonces el complemento absoluto del complemento relativo de : O formalmente: El complemento absoluto de den generalmente no está definido por Otros Universos Exemplos.