Bounded Below Subset of Real Numbers/Examples/Open Interval from 0 to 1
Example of Bounded Below Subset of Real Numbers
Let $I$ be the open real interval defined as:
- $I := \openint 0 1$
However, $I$ does not have a smallest element.
Then $0 < \dfrac x 2 < x$ by Mediant is Between.
Thus $\dfrac x 2 \in I$ but $x > \dfrac x 2$.
So $x$ is not the smallest element of $I$ after all.