the universe is infinitely discrete

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

discuss.

well obviously you since cant define f where for every x, x is not in f(x)
S is then X, an element of P(X),
any arbitrary x  sent to it will always being a member of f(x) = X


consider the set N+{0} and P(N)
suppose there exists a one to one mapping f from N+{0} to P(N)
where 0 --> N,
and x in N ---> f(x) in P(N) | x not in f(x)

S = {x in X | x not in f(x)}
S = {x in N+{0} | x not in f(x)}
S = N+{0}
S is not an element of P(N)