1. The problem asks to write the set represented by the number line from 0 to 4, including points 0,1,2,3,4, with a right arrow at 4. 2. This means the set includes all numbers starting at 0 and going up to and beyond 4 (due to the right arrow), so it is all real numbers $x$ such that $x \geq 0$. 3. In set builder notation, this is written as: $$\{ x : x \geq 0, x \in \mathbb{R} \}$$ 4. Explanation: The colon ":" means "such that". The inequality $x \geq 0$ means all numbers greater than or equal to 0. The symbol $\mathbb{R}$ denotes the set of all real numbers. Final answer: $$\{ x : x \geq 0, x \in \mathbb{R} \}$$