There exists a positive real number $u$ such that $u^3 = 3$
Now if $u^3 \lt 3$, find a real $v \gt u$ such that $v^3 \lt 3$ Then $u$ is not the sup, contradiction. The other way is similar.
There exists a positive real number $u$ such that $u^3 = 3$
Now if $u^3 \lt 3$, find a real $v \gt u$ such that $v^3 \lt 3$ Then $u$ is not the sup, contradiction. The other way is similar.