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High Quality Content by WIKIPEDIA articles! In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a member of the set. For example, the real numbers are closed under subtraction, but the natural numbers are not: 3 and 7 are both natural numbers, but the result of 3 7 is not. Similarly, a set is said to be closed under a collection of operations if it is closed under each of the operations individually.