A half-open interval is a type of interval in mathematics that includes one endpoint but not the other. It is typically represented in the form [a, b), where a is included in the interval, while b is not. This means that all numbers greater than or equal to a and less than b are part of the interval. Half-open intervals are commonly used in various fields, including calculus and statistics, to define ranges of values. They help in specifying limits and boundaries without including the upper limit, which can be useful in scenarios like defining domains for functions or setting conditions in probability distributions.