In mathematics, a set is said to be closed, or have closure, under an operation if performing that operation on every member of the set yields a member of that same set.

For example, the natural numbers are closed under addition. Adding two natural numbers will always produce another natural number. The natural numbers, however, are not closed under subtraction since it is possible to subtract two natural numbers and get a negative (non-natural) number. ie., 1 – 3 = -2

A set is said to be closed under a collection of operations if it is closed under each operation individually.


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