> that's bigger than every natural number in the ZFC sense. I'm not sure what you mean by this. Even for nonstandard models of the natural numbers there will

> that's bigger than every natural number in the ZFC sense. I'm not sure what you mean by this. Even for nonstandard models of the natural numbers there will never be a single number larger than all other numbers, since that violate the Peano axioms. Did you mean by "in the ZFC sense" "the standard model?"