Almost upper bounds for set $\{x:0\le x\le \sqrt{2}\text{ and }x\text{ is rational}\}$

Question

The definition of almost upper bound is this: A number $\alpha$ is said to be an almost upper bound for set $A$ if there exist only finitely many numbers $x$ in $A$ such that $x\ge \alpha$.
Now let $A=\{x:0\le x\le \sqrt 2$ and x is rational$\}$.
I believe that the almost upper bounds for A are $\alpha \ge\sqrt 2$. Since if we take $\alpha =\sqrt 2$, then there is no $x\in A$ such that $x\gt \sqrt 2$ and similarly it can be shown that any $\alpha$ such that $\alpha \gt \sqrt 2$ are also almost upper bounds for A.
However, the book solution mentions the almost upper bounds as $\alpha \gt \sqrt 2$. Can someone please help me? Thanks in advance.