Let $f:\mathbb{R}\to\mathbb{R}$. I was discussing with a another student of my calculus class about the relation between "$f$ achieves its minimum" and "$f$ is bounded from below".
About me the correct answer is:
"$f$ achieves its minimum" $\implies$ "$f$ is bounded from below" (by definition of boundedness from below), but the converse it is not necessarily true.
Could someone please confirm (or not) this thing?
Thank you in advance!