Interval notation is a way of writing subsets of the real number line. It is a shorthand way to write an inequality or system of inequalities, and it is used to describe continuous sets of real numbers by the numbers that bound them. Intervals are written with rectangular brackets or parentheses, and two numbers delimited with a comma. The two numbers are called the endpoints of the interval, where the number on the left denotes the least element or lower bound, and the number on the right denotes the greatest element or upper bound.
There are different types of intervals, including open intervals, closed intervals, half-open intervals, and half-closed intervals. Open intervals do not include their endpoints, while closed intervals include their endpoints. Half-open and half-closed intervals include one endpoint but not the other.
Interval notation can also be used together with the set union operator to write subsets of the number line made up of more than one interval.
Examples of interval notation include:
- Closed interval: [a, b]
- Open interval: (a, b)
- Half-open interval: [a, b) or (a, b]
- Half-closed interval: (a, b] or [a, b)
Overall, interval notation is a useful tool for representing subsets of the real number line in a concise and standardized way.
