User blog comment:Wythagoras/All my stuff/@comment-7484840-20130716082643

You do realise that by saying that ¥^1000(1000) >> Hollom's number, that is equivalent to saying that ¥^1000(1000) >> the combined output of every function that ever has, is or will be defined (possibly including the ¥ function, not sure about it yet, as I think that could send both the ¥ function and the iota function spiralling off to the largest non infinite number) plus a whole load of other recursion over every past iota, happening every Planck time.

Hollom's number is not just uncomputable, but absolutely unknowable (yes I did just make that up), as it refers to the future as well, so even for example I_limit(1) cannot be approximated.

I think functions diagonalising over definability have to do it over a strict set of rules, like rayos number: it diagonalises over a strict set of FOST rules, in which the iota function cannot be defined. Any definablility function that can define the iota function most likely can define itself and many other similar functions, taking it to the largest non infinite number, which may as well be infinity. I believe that the ¥ function comes into this category, but not the iota due to the time variable, and that it diagonalises over things that are defined, not definable.