All I have to do is show from definition that $A$ must have at most one greatest lower bound if $A$ is a subset of $\mathbb{R}$ and is not empty.
My thoughts are if $A$ is not bounded below, then it has no lower bound so no greatest lower bound by definition
And if $A$ is bounded below then there exists a unique $l$ which is a lower bound such that all lower bounds $m$ of $A$ are less than or equal to $l$.
This is just the definition so it doesn't seem right to me, is this Ok? Thanks
Suppose there are two greastest lower bound, $a$ and $b$.
Then for any lower bounds of $A$, $x$, we have $x \le a$. Since $b$ is a lower bound, we have $b \le a$.
By symmetry, we have $a \le b$.
Hence $a=b$.