Bounded Below Subset of Real Numbers/Examples/Real Numbers
Jump to navigation Jump to search
Example of Unbounded Below Subset of Real Numbers
Let $\R$ denote the set of real numbers.
$\R$ is not bounded below.
Let $x \in \R$.
Then there exists $x \in \R$ such that $x$ is a lower bound for $\R$.
- $x - 1 \in \R$ such that $x - 1 < x$
and so $x$ is not a lower bound for $\R$.