Interval

An interval is a subset $I$ of the real numbers such that, for all $x<y\in I$, $xt+(1-t)y$ belongs to $I$ for all $t\in[0,1]$.
Intuitively, $I$ contains every number between two given boundaries. It is hence a convex set.

Examples and remarks

• $[2,5]$ is the set of numbers between 2 and 5, including 2 and 5 (it is a closed interval).
• $(2,5)$ is the set of numbers between 2 and 5, excluding 2 and 5 (it is an open interval).
• $(-\infty,3)$ is the set of numbers less than 3. It is not open, neither closed.