# infinite sets problem

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• Sep 23rd 2010, 09:53 PM
joker40
infinite sets problem
Is it possible to find infinite countable set that is subset of
infinite uncountable set
• Sep 23rd 2010, 10:12 PM
undefined
Quote:

Originally Posted by joker40
Is it possible to find infinite countable set that is subset of
infinite uncountable set

You mean like $\mathbb{Z}\subset\mathbb{R}$?
• Sep 24th 2010, 04:49 AM
joker40
Z
What is Z
• Sep 24th 2010, 05:07 AM
joker40
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
• Sep 24th 2010, 05:19 AM
Plato
Quote:

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 $(0,1)$.
• Sep 24th 2010, 06:55 AM
HallsofIvy
And the set of irrational numbers in (0, 1) is an uncountable proper subset.