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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?

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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.

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