User blog comment:Ikosarakt1/Uncountable function cannot exists/@comment-1605058-20130802172024/@comment-1605058-20130803195511

Even when we can't define some ordinal, it doesn't mean that it doesn't exist. It virtually exists in Von Neumann universe. Yes, that ordinal would be limit of googology, but we still can extend our notations all the way up to this ordinal, using stronger and stronger and more complicated tools.

We can't make \(\omega_1\) function. If it exists, it would be undefinable and nonconstructable. Just as with above ordinal - if it exists, it just exists, that's all we can know from its existence.