User blog comment:Simplicityaboveall/Insanely Fast-Growing Functions/@comment-24920136-20170924204954

There is  a fatal  flaw that really stalls out your functions at epsilon zero level permanently as in, stuck below it.

Namely R. "complete hereditary form" i take it you mean hereditary base 10 notation, which then replaces 10 to omegas. The problem is that finite power towers (ie. size less than omega) will never reach epsilon zero level. thats kind of like the whole point of e_0 in the first place, googologically speaking.

refer to page 11, in which you make a simple but crucial mistake in which you write:

10↑²10 -->  f_2(10)

10^^10 is not hereditary base 10, it's actually knuth's up arrow notation. To write 10^^10 in hereditary base 10 you write a power tower of 10s, 10 high, or alternatively:

10^10^10^10^10^10^10^10^10^10

for which the correct conversion to omegas is

w^w^w^w^w^w^w^w^w^w Or colloquially w^^10, a far cry from e_0

---

Similarily you make another mistake a bit further down with 10^^^10. The correct hereditary form is a very large, but finite, power tower of 10's, so converting tens in the hereditary form of n=10^^^10 will yield w^^x, with x being a very large, but finite number, less than omega. Thus not only do you not reach zeta_0, you don't even reach epsilon_0

I hope my explanation was clear, and i'd like to add this is not a display of being passionate about a subject nor critical to you  as a person. i believe the community benefits from all people trying to create large numbers, but also from helping eachother understand and correct our mistakes.