Let n ≥ 2 {\displaystyle {}n\geq 2} . Show that the norm ‖ x ‖ := max { | x i | : 1 ≤ i ≤ n } {\displaystyle {}\Vert {x}\Vert :=\operatorname {max} \{\vert {x_{i}}\vert :1\leq i\leq n\}} on R n {\displaystyle {}\mathbb {R} ^{n}} does not come from an inner product ⟨ − , − ⟩ {\displaystyle {}\left\langle -,-\right\rangle } .
