## … addition.

A set is closed under *addition* if you can add any two numbers in the set and still have a number in the set as a result.

## … (scalar) multiplication.

A set is closed under (scalar) *multiplication* if you can multiply any two elements, and the result is still a number in the set.

Generally, “closed under *some operation*” means the elements of the set are not being able to “escape” the set using that operation. The result always