# Can an empty set satisfy the definition of a polyhedron?

Based the definition, a polyhedron satisfies {$x \in \Re^n |Ax \ge b$} . But can an empty set satisfies this? In another word, is an empty set also a polyhedron?

The set $\{\,x\in\Bbb R^1\mid Ax\ge b\,\}$, where $A=\begin{pmatrix}1\\-1\end{pmatrix}$ and $b=\begin{pmatrix}1\\1\end{pmatrix}$, is empty.