Define $A = \{ 1,2,A \}$, $A$ can not be a set (Axiom of regularity). Can $A$ be a "class" or a "collection" of elements. This question is probably very naive but it does bother me and I am not sure where to look for an answer.
Define $A = \{ 1,2,A \}$, $A$ can not be a set (Axiom of regularity). Can $A$ be a "class" or a "collection" of elements. Suppose it is. Don't we get the Russel's paradox again? Take the collection of all collections which does not contain themselves as an element. Does it contain itself as an element?
Is there a short answer or is there a lot of knowledge involved?
Thank you  
Remark: I know that $A$ cannot be a set because of axiom of regilarity. But, what prevents it from being a class or a collection?

Luiz Cordeiro already mentioned that you can't define $A$ like this,
but as you are interested in the details of axiomatic set theory let
me try to explain why exactly you can't do it.
You will know that in ZFC $\{a,b\}$ is just an abbreviation.  You
usually introduce the pairing axiom which says that for any sets $a$
and $b$ there's a (unique) set which contains exactly the elements $a$
and $b$.  This unique set is then written as $\{a,b\}$ and it is
obvious how this can be extended to one or (using union) three
elements.
So, when we later write something like "let $A$ be the set
$\{1,2,c\}$" we are actually applying a couple of axioms under the
assumption that $1$, $2$, and $c$ are sets.  What we should
have said is: "We know that $1$, $2$, and $c$ are sets and by the
axioms of pairing, union, and extensionality we know there's a unique
set which has exactly these three elements.  We'll call it
$A$."
Now it should be clear why this fails for the attempted "definition"
of your $A$ above.  The step "we know that $1$, $2$, and $A$ are sets"
doesn't work because at this point $A$ hasn't been defined yet.
