Russell's paradox dilemma

Hi,

I have a problem with "Russell's paradox" which I have just learned about at school. Simply said, it means that:

Let's say we have sets *R* and **A**. And according to Russell's paradox (or theory) there cannot exist such set **R**, that:

$\displaystyle R = \{ A \ | \ A \notin A \}$

But I think that such set "**exist**"...

What exactly means that $\displaystyle A \in A$? Then the set **A** could be one of these:

$\displaystyle A = \{ a, \ b, \ c, \ A \}$

$\displaystyle A = \{ 4, \ 6, \ A, \ 9 \}$

$\displaystyle A = \{ A, \ "string1", \ "string2" \}$

And what means that $\displaystyle A \notin A$? Then the set **A** could be one of these:

$\displaystyle A = \{ a, \ b, \ c, \}$

$\displaystyle A = \{ 4, \ 6, \ 9 \}$

$\displaystyle A = \{ "string1", \ "string2" \}$

So let's say that $\displaystyle A = \{a, \ b, \ c\}$.

Then:

$\displaystyle R = \{\{a, \ b, \ c\}, \ \{a, \ b, \ c\}, \ \{a, \ b, \ c\}, \ ...\}$

...so **I have found** such set **R** that:

$\displaystyle R = \{ A \ | \ A \notin A \}$

So where is the paradox (Thinking) ?

Thanks.