Is it possible to find infinite countable set that is subset of
infinite uncountable set
for example infinite countable set of set (0,1) . I need to find infinite countable set of that is subset of (0,1) and also uncountable set that is proper subset of (0,1)
every text book have example of proving set (0,1) is infinite uncountable. But I am lost how to find these 2 things. I think it trows me of because (0,1) is uncountable
It is difficult to read and understand that question.
It is the case that the set $\displaystyle (0,1)$ in indeed uncountable.
The set of rational numbers, $\displaystyle \mathbb{Q}$, is countable.
Any subset of a countable set is countable.
So $\displaystyle \mathbb{Q} \cap (0,1)$ is a countable subset of $\displaystyle (0,1)$.