An open interval is a range of numbers that does not include its endpoints. It is typically represented in mathematical notation as (a, b) , where a and b are the lower and upper bounds, respectively. This means that all numbers greater than a and less than b are part of the interval, but a and b themselves are not included. Open intervals are commonly used in calculus and real analysis to describe sets of real numbers. They help in defining concepts such as limits and continuity. Understanding open intervals is essential for studying functions and their behaviors within specific ranges, contributing to various fields like mathematics, physics, and engineering.