Definition:Real Interval/Unit Interval

Definition
Some authors use $\mathbf I$ specifically to mean the (closed) unit interval, that is, the closed interval from $0$ to $1$:
 * $\mathbf I := \left [{0 \,.\,.\, 1} \right] = \left\{{x \in \R: 0 \le x \le 1}\right\}$

When referring to the unit interval, it is usually understood that the closed unit interval $\left [{0 \,.\,.\, 1} \right]$ is meant.

Otherwise, the interval $\left ({0 \,.\,.\, 1} \right)$ is referred to as the open unit interval.