<Table> <Tr> <Td> </Td> <Td> This article relies largely or entirely on a single source . Relevant discussion may be found on the talk page . Please help improve this article by introducing citations to additional sources . (June 2013) </Td> </Tr> </Table> <Tr> <Td> </Td> <Td> This article relies largely or entirely on a single source . Relevant discussion may be found on the talk page . Please help improve this article by introducing citations to additional sources . (June 2013) </Td> </Tr> <P> 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 positive integers are closed under addition, but not under subtraction: 1 − 2 (\ displaystyle 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 (\ displaystyle 0 + 0 = 0), 0 − 0 = 0 (\ displaystyle 0 - 0 = 0), and 0 × 0 = 0 (\ displaystyle 0 \ times (0) = 0)). </P> <P> Similarly, a set is said to be closed under a collection of operations if it is closed under each of the operations individually . </P>

When is a set closed under an operation