Let S be a bounded set that is not empty.

Prove that sup(S) is a boundary point of S

can someone help me complete this proof? i've been trying for a long time and i can't come up with anything other than

If S is a (not empty) set of real numbers and S has an upper bound y,

then there is a least upper bound of the set S.

That least upper bound is also called the supremum of S

please help, i really need it