If you know that a given set O is countable.
$\#O\leq \#\mathbb{N}$
Does this imply that the following statement holds?
$\# O \leq \#\mathbb{R}$
I'm not sure, but I think it makes sense, because $\mathbb{N}\subset\mathbb{R}$ and therefore you can construct easily an injective function between $\mathbb{R}$ and $\mathbb{N}$.