Closure theorem

The Closure Theorem in mathematics states that when you perform certain operations—like addition, subtraction, multiplication, or division—on numbers within a specific set, the result will also be within that same set. For example, the set of integers (whole numbers) is closed under addition because adding any two integers always results in another integer. Similarly, the set of real numbers is closed under these operations. Essentially, the theorem assures us that these operations keep us "inside" the set, maintaining consistency and predictability within that system.