3 ms·
You can find a natural number that is bigger than any one natural number, but you can't write one down that's bigger than every natural number in the ZFC sense.
by hypersoar 5y ago
You can find a natural number that is bigger than any one natural number, but you can't write one down that's bigger than every natural number in the ZFC sense.
- dwohnitmok 5y ago> 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?"
- gooberwonder 5y ago45,000,000,001?
- agalunar 5y agoLook around you!
- munk-a 5y agoDo you mean that given finite resources (like time and matter) we would be unable to express the number? Or are you talking about a sort of recursive thing where writing down a number which is a sum of all natural numbers up to and including itself is impossible since that number is bigger each time you look at it?