To describe the set where y is nonnegative, we need to establish the inequality that represents this condition. A nonnegative number is defined as any number that is greater than or equal to zero. Thus, we can express this mathematically as:
y ≥ 0
This inequality tells us that y can be zero or any positive number.
Now, let’s convert this inequality into interval notation. In interval notation, we express the set of all nonnegative numbers as:
[0, ∞)
Here, [0 indicates that zero is included in the set (as the square bracket means the endpoint is included), and ∞) indicates that there is no upper limit to y (as infinity is not a number but represents unbounded growth).
In summary, the set of all nonnegative values of y can be succinctly described using both the inequality and interval notation:
- Inequality: y ≥ 0
- Interval Notation: [0, ∞)