Adding (or multiplying) two numbers gives a number. True also for subtraction. Also true for division, with division by zero excluded.

 

One good pedagogical tool is giving a counterexample. To help clarify this concept, consider numbers 0..10. If we add 2 + 3, using our fingers, we get 5. If we add

5 + 7, we have no more fingers. Therefore, using only our fingers does not obey closure. There are an infinite number of real numbers, and so closure is met.