User blog comment:Hyp cos/Growth Rate ε(0)−1/@comment-30754445-20170714141844/@comment-11227630-20170714162441

What about this "linear approximation"?

$$f\ge^*g$$ if there exists a and b such that for all n > 0, $$f(an+b)\ge g(n)$$

$$f\approx g$$ if $$f\ge^*g$$ and $$g\ge^*f$$

Then 2↑↑n, "n in a square" and $$f_3(n)$$ are comparable. 2^n and $$f_2(n)$$ are comparable, but n^n isn't comparable to those two.