User blog comment:Cookiefonster/FGH growth rate stuff/@comment-2033667-20150918193817/@comment-5150073-20150919040726

There is a formal alternative: instead of "approximating" growth rate, use bounding growth rate (let's say growth rate = eventual domination). For, say, Goodstein function, we can use f_a(n,WH) [<] G(n) [<] f_e_0(n,WH), where a is any ordinal < e_0. WH in the second argument indicates that fundamental sequences are from Wainer hierarchy.