I'm trying to delve into the lovely world of linear programming and have been confronted by a small confusion. If we let
$$X = \{ x \in \mathbb R^n \mid a^\top x = b\}$$
and $a$ in the set Real vectors of length $n$, and $b$ in the set of real numbers... how do we prove that $X$ will have no extreme points if $n \geq 2$. I understand the logic with straight lines, but I'm really not too sure how to go about proving it. Thank you for the help :)