You don't have to use those words. For instance, for n >> k >> ln(n) >> 1, he says "Specifically, we require n much greater than k much greater than log n muc

You don't have to use those words. For instance, for n >> k >> ln(n) >> 1, he says "Specifically, we require n much greater than k much greater than log n much greater than one", and says it's unwieldy. Well, if you say it like that, then it is. "Specifically, we require than the magnitudes of n, k, log n, and one be in decreasing order with significant distance between each." Not a problem. Just don't try to read notation literally in the order it's written.