User blog comment:Vel!/FGH Gripe/@comment-30118230-20170220112412/@comment-30754445-20170220182214

The intuitive idea of "comparable growth" existed before I created my definition. All I did was to translate an intuitive idea into a more rigorous language.

And just because that phrase didn't have a precise definition until now, doesn't mean it was completely meaningless. The intuitive meaning of "a growth-rate comparable to ε₀ in the FGH" is that the values of our function can be approximated with f_ε₀(n) with reasonable values of n. This is terribly imprecise, of-course, but the intutive gist of what it means is perfectly clear.