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?

A class in standard (ZF) set theory generally coincides with a property that any set may or may not have.  For instance, the property might be "$\phi(x) \equiv x \not\in x$".  Then $\{x \;:\; x\not\in x\}$, while not necessarily a set, is a well-defined class.  But note that the elements of a class are sets, not classes.  In your case, you want to know whether there is a class corresponding to $A$.  Such a class would contain exactly $1$, $2$, and a third set equal to the entire class.  This could only occur if $A$ were itself a set, which you've already noted is ruled out by the axiom of regularity.
