[Math] How to a set be bounded and countably infinite at the same time

Question

There is a theorem in my textbook that states,

Let $E$ be a bounded measurable set of real numbers. Suppose there is a bounded countably infinite set of real numbers $\Lambda$ for which the collection of translates of $E$, $\{\lambda + E\}_{\lambda \in \Lambda}$, is disjoint. Then $m(E) = 0$.

I'm a little confused about this theorem, because it's saying that a set is bounded and countably infinite at the same time. But if a set is bounded, isn't it supposed to be finite?

Thanks in advance

Answer 1

The set $\{2^{-k}\ |\ k \in \mathbb{Z}^+\}$ is bounded and countably infinite.