What does the closure property state about a set?

The closure property refers to a fundamental characteristic of certain mathematical operations within a set. Specifically, it states that when you apply a particular operation (such as addition, subtraction, multiplication, or division) to elements of a set, the result will always produce an element that remains within the same set.

For example, consider the set of integers and the operation of addition. If you add any two integers, the result is always another integer; hence, the set of integers is closed under addition. This illustrates that the operation does not lead to an element outside of the initial set.

This property is crucial in understanding the structure of mathematical sets and their operations, as it confirms that the operation does not yield any unexpected elements outside the predefined boundaries of the set.