the definition of closure property
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A set is closed under an operation if performance of that operation on members of the set always produces a member of that set. For example, the positive integers are closed under addition, but not under subtraction: is not a positive integer even though both 1 and 2 are positive integers
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A set that is closed under an operation or collection of operations is said to satisfy a closure property. Often a closure property is introduced as an axiom, which is then usually called the axiom of closure. ... For example, the set of even integers is closed under addition, but the set of odd integers is not.
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