Answer
Proof given below.
Work Step by Step
Every least upper bound is an upper bound.
Let $M_{1}$ and $M_{2}$ be least upper bounds.
Taking $M_{1}$ to be a least upper bound
and $M_{2}$ to be just an upper bound, we can write
$M_{1}\leq M_{2}$
Now, taking $M_{2}$ to be a least upper bound
and $M_{1}$ to be just an upper bound, we can write
$M_{2}\leq M_{1}$
By properties of real numbers,
$(M_{1}\leq M_{2})$ and $(M_{2}\leq M_{1})\quad \Leftrightarrow\quad M_{1}=M_{2}$.
There can only be one.
