Interval

Definition

An interval is a continuous range of values, such as all of the real numbers between $-2$ and $0,$ inclusive. The most common uses of an interval are to specify the domain and range of a function.

Symbols

If an interval has either $($ or $)$ in it, the values at the end are NOT included in the interval.

If an interval has either $[$ or $]$ in it, the values at the end ARE included.

If both endpoints are not included, then the interval is open. If both endpoints are included, then the interval is closed.

Note: The symbols $($ and $)$ are used with $-\infty$ and $\infty,$ by convention.

Examples

• $(2,3)$ means all real numbers between $2$ and $3,$ but not including $2$ or $3.$
• $[-2,0)$ means all real numbers between $-2$ and $0,$ including $-2,$ but not including $0.$
• $[5, \infty)$ means all real numbers greater than or equal to $5.$

Use latex \infty for infinity symbol and use latex \cup for OR symbol.