Math CentralQuandaries & Queries


Question from Bhavya, a student:
Dear Sir/Ma'am,
I read in the text book that the growth rates of these 3 functions are as below-
n2/3 < n/lg n < n0.99


How far can you throw that textbook? Go give it a try and then come back when you're finished for the answer. No, don't: first find out at what power of n less than 1 they do think the transition happens, tell me, then go see how far you can chuck it. I'm curious <grin>

In fact, for any a<1<b, and any k>0, we have

na < n/(lg(n)k) < n < n (lg(n)k) < nb

and in particular n0.99 < n/lg(n).

You are quite right that these matters are hard to check on a calculator. The logarithm grows exceedingly slowly!

Good Hunting!


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