User blog comment:Wythagoras/All my stuff/@comment-10429372-20130718073726/@comment-5529393-20130718164520

I don't see where Wythagoras said that ¥(n) would be the largest possible output of any function;  obviously, there is no largest possible output, as f(n) = m can be defined for any m. But it seems reasonable that "the largest number definable in n characters" can define a definite function, so long as the allowed definitions cannot refer to "definable" themselves. (I think Wytahgoras should add that clause to his definition.)

I'm trying to interpret your second post;  if you mean that the number z(1000) is defined by a 2003 character definition that does not refer to "definability", yes, that is true. But you still can't refer to the z function in general, so you can't refer to z^1000(n) unless you use 2 z^999(n) + 3 characters. I'm not getting your point at all.