Bounded Below Subset of Real Numbers/Examples/Closed Interval from 0 to 1

Let $I$ be the closed real interval defined as:
$I := \closedint 0 1$
Then $I$ is bounded below by, for example, $0$, $-1$ and $-2$, of which $0$ is the infimum.
$I$ is also the smallest element of $I$.