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

infinite uncountable set

Printable View

- Sep 23rd 2010, 08:53 PMjoker40infinite sets problem
Is it possible to find infinite countable set that is subset of

infinite uncountable set - Sep 23rd 2010, 09:12 PMundefined
- Sep 24th 2010, 03:49 AMjoker40Z
What is Z

- Sep 24th 2010, 04:07 AMjoker40for 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 - Sep 24th 2010, 04:19 AMPlato
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 $\displaystyle (0,1)$. - Sep 24th 2010, 05:55 AMHallsofIvy
And the set of

**irrational**numbers in (0, 1) is an uncountable proper subset.