I cannot use the subset notation. We can only use the "element of". That is our only operator in the universe we are using.
Well, yes, Zermelo–Fraenkel set theory has only two predicates: equality and membership. However, is easily expressible as . Subset relation is used in the axiom of power set.
Last edited by emakarov; June 29th 2012 at 04:30 PM.
in this case, i would be tempted to prove the contrapositive: distinct sets give rise to distinct power sets. you can use the same argument as in Plato's post: