How to show that this set is bounded? Given set $\{3 - x \mid x &lt; 0\}$, find if it is bounded.


So, from intuition it should be bounded from below, but how to show it?
If $x&lt;0$ then $3-x&gt;3$, so the set in question is the open interval $(3,\infty)$. Hence it is bounded below (by $3$ for instance) but not above.
Proof without words in this plot.