Heine Borel Theorem statement (a) I have been following Prof Winston Ou's course on analysis on Youtube.
In the lecture on Heine Borel theorem, he mentioned that a set $E$ in $\mathbb R$ is closed and bounded implies that $E$ is a k-cell (hence $E$ is compact).
I don't understand how he came to this conclusion. For instance, I imagine $E$ could be a discrete set (and still being closed and bounded), but it will not be a k-cell. I would be very grateful if anyone could enlighten me.

He means $D$ will be contained in a $k$-cell, and as $k$-cells are compact and $E$ is still a closed subset of it, it will also be compact.
The boundedness in Euclidean space/metric forces the set inside a product of compact intervals..
