Yes. There exist numbers that cannot actually be written down because they are too big. But you get there by a path of increasing fuzziness, and no clear bound

Yes. There exist numbers that cannot actually be written down because they are too big. But you get there by a path of increasing fuzziness, and no clear boundaries, from numbers that we can both write down, and work with. Then there is a jump to numbers that cannot be written down. Not even in principle. Some people feel that that jump matters. Others don't. I feel it matters. But I accept that most mathematicians, don't.