User blog comment:Wythagoras/All my stuff/@comment-7484840-20130715121715

The ¥ function cannot surpass the iota function for four reasons: One: the iota function cannot be described in symbols in a strict mathematical sense.

Two: even if it could be described in symbols, so could a function very similar to the ¥ function itself, effectively leading it off to the whole 'largest non-infinite number with no other conditions' thing in the ¥ function. Three: the ¥ function is now, if not before, within the iota function set.

And four: Hollom's number doesn't have a definite value yet: it is the final limit of the iota function at the end of the universe, and so will include every function that creates definite numbers ever made, making it effectively unbeatable without breaking the gentleman's rule.