User blog comment:Simplicityaboveall/Extremely Large Numbers 4/@comment-28606698-20160801212403/@comment-25912386-20160802082833

Thanks for your comment Denis !

I agree with you that FGH usually use the rules you mentionned but from https://en.wikipedia.org/wiki/Fast-growing_hierarchy, it is mentionned :

" Generalizing the above definition even further, a  fast iteration hierarchy is obtained by taking  f0  to be any increasing function g:  N →  N. "  It is written " any increasing function " and not just   !! This applies to Deedlit11 's comment too.

"  " does not imply only Knuth arrows as Deedlit11 said'

This also applies to LittlePeng9 who believes that the FGH is uniquely defined with

"  ".

f0  CAN BE ANY INCREASING FUNCTION ! And "   " is very usefull and practical !