Upper Bound and Lower Bounds

None of the sets $\displaystyle \mathbb{Z}, \mathbb{Q}$, and $\displaystyle \mathbb{N}$ is bounded above. The $\displaystyle \mathbb{N}$ is bounded below;$\displaystyle 1$ is a lower bound for $\displaystyle \mathbb{N}$ and so is any number less than $\displaystyle 1$. In fact, $\displaystyle 1$ is the larges or greatest lower bound.

Question: How could there be a number less than $\displaystyle 1$ when $\displaystyle 1$ is the smallest number in $\displaystyle \mathbb{N}$?