Open Real Interval is Subset of Closed Real Interval
Let $a, b \in \R$ be real numbers.
- $\openint a b \subseteq \closedint a b$
- $\openint a b$ is the open interval between $a$ and $b$
- $\closedint a b$ is the closed interval between $a$ and $b$.
Let $x \in \openint a b$.
Then by definition of open interval:
- $a < x < b$
- $a \le x \le b$
and so by definition of closed interval:
- $x \in \closedint a b$