What is the meaning of set builder notation in math?

Set builder notation is a mathematical shorthand used to describe a set by specifying a property that its members must satisfy. It typically takes the form ({x \mid P(x)}), where (x) represents the elements of the set, and (P(x)) is a condition or predicate that defines which elements belong to the set. This notation allows for concise representation of sets, especially when dealing with infinite sets or complex conditions. For example, ({x \mid x > 0}) represents all positive numbers.