Closed Interval: A closed interval includes its endpoints, so it's like having a rope tied across the edges of the dance floor, restricting movement beyond those points.
Half-Open Interval: A half-open interval includes one endpoint but not the other. It's like having one side of the dance floor blocked by a wall, allowing movement only from one direction.
Infinite Interval: An infinite interval extends indefinitely in one or both directions. It's like having an endless dance floor that stretches as far as you can see in either direction.