What is a Set closed under multiplication?

Answer 1

A set is said to be closed under multiplication if, for any two elements ( a ) and ( b ) within that set, the product ( a \times b ) is also an element of the same set. This property ensures that multiplying any two members of the set does not produce an element outside of it. For example, the set of integers is closed under multiplication because the product of any two integers is always an integer. In contrast, the set of positive integers is also closed under multiplication for the same reason.