User blog comment:Simplicityaboveall/The Construction of Extremely Large Numbers/@comment-24920136-20160728195542/@comment-24920136-20160729155220

i just really like the largest numbers games i am not really a mathematician nor a theorist.

I don't want to sound rude or discouraging, im always happy when i see a new person show up with their creation i was specially intrigued by this one since you penned it all by hand (i bet there must be alot of rolled up papers in your discard bin!) it was a good read and i really hope you update it and come up with a Version 2

Just letting you know, ε0= ω^^ ω is not actually standard stuff

There even might be people that consider ε0= ω^^ ω as abuse of notation or even undefined.

ε1 is a whole other ballpark. remember that above ε0 theres ambiguity in all ordinals, ie. some can have two or more valid common fundamental sequences and if you are using ordinals for a hierarchy then it really really matters which one you take.

ε1 = ε0 ^^ 1, ε0 ^^ 2, ε0 ^^ 3,... is just one comonly used sequence

theres also

ω ^ε0+1, ω ^ ω ^ ε0+1, ω ^ ω ^ ω ^ ε0+1...

And same index does not give you same ordinal on these.