Interval Notation

Writing Sets of Numbers

When we describe a range of numbers, we use interval notation.

It’s a compact way to write “all numbers between A and B.”

The Key Idea

  • Square bracket [ or ] means the endpoint is included
  • Parenthesis ( or ) means the endpoint is excluded

On a number line:

  • Filled dot = included
  • Hollow dot = excluded

Why Parentheses for Infinity?

Infinity isn’t a real number. You can’t actually reach it.

So we always use a parenthesis: (−∞,5](- \infty, 5] or [0,∞)[0, \infty)

Never write [∞[\infty or −∞]-\infty]

Common Intervals

All real numbers:

(−∞,∞)(-\infty, \infty)

All non-negative numbers:

[0,∞)[0, \infty)

All positive numbers:

(0,∞)(0, \infty)