Definition talk:Epsilon Relation

There are a load of things going wrong here. The definition of $E$ is not void, but I second strongly the third point made, i.e. what is the use of $E$ over $\in$. Furthermore, things like Epsilon is Foundational are (at least for the moment) void as a relation (and any relational structure) demands a set to work on, while the $A$ in consideration is a class.

The second point is not a problem however (the statement in parentheses), because it is simply void (or at best: yet to be defined how) to talk about $(x,y)\in E$ if $E$ is a class. If $E$ is a set, no problem arises.

I would say, in general, that the ZF(C) axioms tell us how to use the formal symbol $\epsilon$ (more precisely: the binary function symbol $\epsilon$) of our language in correspondence to everything else. The need for $E$ is at the moment not clear to me. Hopefully, someone can elucidate me on this point. --Lord_Farin 03:36, 26 November 2011 (CST)