Two norms $\| x \|_\alpha$ and $\| x \|_\beta$ are said to be equivalent if there exists positive real numbers $C$ and $D$ such that
$C\|x\|_\alpha\leq\|x\|_\beta\leq D\|x\|_\alpha$
does this mean that there also exists positive real numbers $E$ and $F$ such that
$E\|x\|_\beta\leq\|x\|_\alpha\leq F\|x\|_\beta \qquad ?$