I'm asked to verify if the following set is polyhedral,
$$ X = \{[x_1;x_2]: min(x_1,x_2) \leq 0\}$$
Definition of a polyhedral set,
A set $Y$ is polyhedral if $Y = \{y: Ay \leq b\}$, for finite $A$ and $b$.
I think that it isn't polyhedral but I'm not sure how to go about proving it. By looking at the feasible space we can see that it fills up 3 quadrants (the second, third and fourth) and I believe we can't represent this as a finite number of inequalities in $x_1$ and $x_2$.
I also tried introducing a slack variable $\tau$ such that,
$$ \begin{split} min(x_1,x_2) &\leq \tau \\ \tau &\leq 0 \end{split} $$
But in this case we'll need to introduce some branching constraints to select which one of $x_1$ and $x_2$ is the minimum and less than $\tau$.
Could someone give me pointers on how to approach this?