1. The problem is to understand what builder notation is in mathematics. 2. Builder notation is a way to describe a set by specifying the properties that its members must satisfy. 3. The general form is $\{x \mid P(x)\}$, which reads as "the set of all $x$ such that $P(x)$ is true." 4. For example, $\{x \mid x > 0\}$ means the set of all $x$ such that $x$ is greater than zero. 5. This notation helps define sets without listing all elements explicitly, especially useful for infinite or large sets. 6. Remember, the vertical bar $\mid$ means "such that," and $P(x)$ is a condition or property. 7. Builder notation is also called set-builder notation and is fundamental in set theory and algebra. 8. In summary, builder notation describes sets by stating the properties elements must have.