1. ## infinite sets problem

Is it possible to find infinite countable set that is subset of
infinite uncountable set

2. Originally Posted by joker40
Is it possible to find infinite countable set that is subset of
infinite uncountable set
You mean like $\mathbb{Z}\subset\mathbb{R}$?

What is Z

4. ## for example

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

5. Originally Posted by joker40
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 $(0,1)$ in indeed uncountable.
The set of rational numbers, $\mathbb{Q}$, is countable.
Any subset of a countable set is countable.
So $\mathbb{Q} \cap (0,1)$ is a countable subset of $(0,1)$.

6. And the set of irrational numbers in (0, 1) is an uncountable proper subset.