Closure (mathematics)

A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation. For example, the integers are closed under subtraction, but the positive integers are not: $1 - 2$ is not a positive integer even though both 1 and 2 are positive integers. Another example is the set containing only zero, which is closed under addition, subtraction and multiplication (because $0+0=0$ , $0-0=0$ , and $0\times{0}=0$ ).

单词	P closure
释义	P closure 英语百科 Closure (mathematics) A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation. For example, the integers are closed under subtraction, but the positive integers are not: $1 - 2$ is not a positive integer even though both 1 and 2 are positive integers. Another example is the set containing only zero, which is closed under addition, subtraction and multiplication (because $0+0=0$ , $0-0=0$ , and $0\times{0}=0$ ).
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P closure

Closure (mathematics)