Definition
An interval is a subset of The Real Numbers that contains all real numbers lying between any two numbers of the subset.
Endpoints
The endpoints of an interval are its supremum, and its infimum, if they exist as real numbers. If the infimum does not exist, one says often that the corresponding endpoint is
Types of Intervals
An open interval does not include any endpoint, and is indicated with parentheses, Whereas a closed interval is an interval that includes all its endpoints and is denoted with square brackets. A half-open interval has two endpoints and includes only one of them. It is said left-open or right-open depending on whether the excluded endpoint is on the left or on the right