1. Let's start by understanding what an open interval is in mathematics. 2. An open interval between two numbers $a$ and $b$ is written as $\left(a,b\right)$. 3. This interval includes all numbers greater than $a$ and less than $b$, but it does not include $a$ and $b$ themselves. 4. For example, the open interval $\left(1,5\right)$ includes numbers like 1.1, 2.5, and 4.999 but not 1 or 5. 5. The term "open" indicates that the endpoints are not part of the interval, distinguishing it from a closed interval $\left[a,b\right]$, which does include the endpoints. 6. Open intervals are useful in calculus and other areas of mathematics where we focus on values strictly between two points. Final answer: An open interval $\left(a,b\right)$ includes all real numbers $x$ such that $a < x < b$, excluding the endpoints $a$ and $b$.