the universe is infinitely discrete

and the set of reals is in one to one correspondence with the set of naturals.

discuss.

| x not in f(x)
"such that x is not a member of f(x)"
f is supposed to be a bijective mapping.  all im saying, is obviously youre going to have at least one x that is mapped to a subset that contains itself, since one of the subsets is the entire set.
my point was that if somehow you managed to create a map that satisfied that condition, it would imply that S is equal to the entire set.  thats because you wouldnt have mapped something to the whole set.
my argument is not that S is not contradictory, but that its not a valid method because of its similarity to russel's paradox.  i thought the ZFC axioms denied the ability to construct a set like that?

my other bit about 0 is that if you added one more element, but used the powerset of the set without that element, you could point that to the complete set and not bother with S.  youre obviously not mapping a set to its own powerset then, but the cardinality implications dont get affected, since the set of naturals is countably infinite whether you put {0} in or not.