<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> 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>
when is a set closed under an operation
when is a set closed under an operation
if performance of that operation on members of the set always produces a member of the same set
if performance of that operation on members of the set always produces a member of the same set