User blog comment:Wythagoras/All my stuff/@comment-10429372-20130718073726/@comment-5529393-20130718180249

Yes, the condition that ¥ cannot use the ¥ function is not sufficient. I believe the condition should be that any definition cannot use the notion of definable. Do you have a problem with the ¥ function with that condition?

You said:

"However, for any finite output possibility for the ¥ function, there will always be a larger possible finite output. This means it's condition for the largest possible output cannot possibly be furfilled and therefore, as with the z function, the ¥ function cannot take on a value."

That's what I was having an issue with, there is no condition that the ¥ has the largest possible output. It is the largest number definable in n characters, and there are only finitely many n character strings, so there cannot "always be a larger possible finite output."

If you concede that the ¥ function can be a definite function, then there is no problem. The fact that there can always be a larger function is not a problem for the ¥ function;  it's just the way things are.