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Interval notation is a mathematical way to describe a range of values. In general, it is expressed by two endpoints, which define the interval's beginning and end. The notation uses either parentheses or square brackets to specify whether the endpoints are included or not:

• Parentheses \( () \) indicate that the endpoints are not included, called an open interval.
• Square brackets \[ [] \] imply that the endpoints are included, referred to as a closed interval.

For example, the interval \((-2, 2)\) specifies all numbers between -2 and 2, excluding -2 and 2 themselves. This is an open interval. When dealing with open intervals, always remember that the boundaries are not part of the set. Using interval notation helps to concisely express a set of values, especially when stating output or solution sets for functions, inequalities, or within calculus. In this format, it's clear and precise, eliminating the need for lengthy descriptions.

Inequality representation is another way to express the range of values described by an interval. When transforming an interval, like \((-2, 2)\), into inequality notation, we weaken our language to say what numbers are greater or less than specific points:
For \((-2, 2)\), the inequality notation is \(-2 < x < 2\). This compound inequality tells us several things:

• \