[kevinwang]

Nitpicky/not important, but they say:

Since loglog(n) tends to infinity with n, the additional term in the exponent tends to 0, meaning these constructions achieve growth only slightly faster than linear.

Would anyone else describe the previous asymptotic behavior like that? I mean obviously loglogn to O(1) is a quantum leap, but wouldn't you describe loglogn as "grows so slowly it's almost constant", so the constructions achieve growth "almost n^{1+c}"? But I guess that might be overcorrecting too hard.

[kevinwang]

Just reread this comment and it's not easy to understand, but the edit window is passed.

What I meant is that they describe loglogn the same way you could describe O(n) or O(n^2) -- it "tends to infinity with n", even though my mental model for loglogn is to treat it as barely more than constant. See: https://cs.stackexchange.com/questions/148197/who-said-first...