Show that we may replace $($N$2)$ by

$||x||=0,$Longrightarrow,$x=0$

without altering the concept of a norm. Show that nonnegativity of a

norm also follows from $($N$3)$ and $($N$4).$

$($N$2)$

$||x||=0$

Longleftrightarrow

$x$