Definition:Closed Interval

Let $$\left({S; \le}\right)$$ be a totally ordered set.

Let $$m, n \in S$$. Then the closed interval between $$m$$ and $$n$$ is denoted and defined as:

$$\left[{m \,. \, . \, n}\right] = \left\{{x \in S: m \le x \land x \le n}\right\}$$

$$n < m$$ iff $$\left[{m \,. \, . \, n}\right] = \varnothing$$.

This notation is a fairly recent innovation, and was introduced by C. A. R. Hoare and Lyle Ramshaw.

The older notation, which is more frequently seen, is $$\left[{m, n}\right]$$. However, it can easily be confused with other usages of the same or similar notation, so its use is deprecated.