Prove that $\sup[0,1] =1$ Alongside the question in the title, does it matter if the question is $(0,1)$ or $[0,1)$?
I know that it satisfies the first condition, $1$ is an upper bound but I am not sure where to go from there.
Thanks.

A number $a$ is supremum of a set $A$ if 


*

*$a\geq x$, for all $x\in A$

*If $b\geq x$, for all $x\in A$, then $a\leq b$.


By definition of supremum, $1= \sup(0,1)=\sup[0,1)=\sup[0,1]$.
