User blog comment:KthulhuHimself/Library Function/@comment-25601061-20151114193547

Lib(n) function is beyond all other functions, and beyond all FGH, so it reaches limit of FGH. Since FGH only allows countable ordinals, then we cannot measure the growth rate of Lib(n), because there cannot be uncountable ordinals in FGH. So we can create a new countable ordinal, beyond all other countable ordinals (we will call this hyper-countable ordinal), and call this L0, which can be defined as:

L0[n] = the largest countable ordinal which can be defined in  α symbols

L0 =  L0[ ω ]

Therefore we have a new ordinal, which works as a countable ordinal, so it's valid in FGH. So we have growth rate of Lib(n) function similar to fL 0 (n).