Closure

A set has Closure to an operation if we can take that operation and perform it on any two members of the set, and we get a result that is also a member of the set.

Let S be a set, S={-1,+1} and let our operation be multiplication and we use the symbol *:

-1*-1=+1

+1*-1=-1

We also need to check “duplicates”:

-1*-1=+1

+1*+1=-1

Now are done with the multiplication. We scan through all our answers and see that every time the answer is either -1 or +1 and both of these are in S, so we can declare that “S is closed to multiplication” or we might word it as “S has Closure with respect to multiplication”.