\begin{definition}[Definition:Real Interval/Unit Interval]
A '''unit interval''' is a real interval whose endpoints are $0$ and $1$:
{{begin-eqn}}
{{eqn | l = \openint 0 1
      | o = :=
      | r = \set {x \in \R: 0 < x < 1}
}}
{{eqn | l = \hointr 0 1
      | o = :=
      | r = \set {x \in \R: 0 \le x < 1}
}}
{{eqn | l = \hointl 0 1
      | o = :=
      | r = \set {x \in \R: 0 < x \le 1}
}}
{{eqn | l = \closedint 0 1
      | o = :=
      | r = \set {x \in \R: 0 \le x \le 1}
}}
{{end-eqn}}
\end{definition}