Interval Notation

Interval notation is a mathematical notation used to represent a range of values on the number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

The notation \( (a, b) \) represents an open interval, meaning that the endpoints \( a \) and \( b \) are not included in the interval.

The notation \( [a, b] \) represents a closed interval, meaning that the endpoints \( a \) and \( b \) are included in the interval.

The notation \( (-\infty, a) \) represents all real numbers less than \( a \), with \( a \) not included.

The notation \( [a, \infty) \) represents all real numbers greater than or equal to \( a \), with \( a \) included.

A closed dot indicates that the endpoint is included in the solution set, used for symbols \( \leq \) and \( \geq \).

An open dot indicates that the endpoint is not included in the solution set, used for symbols \( < \) and \( > \).

The inequality notation is \( x \leq 0 \).

The inequality notation is \( 3 \leq x < 7 \).

No, you cannot use the symbols [ or ] with infinity in interval notation.