In the CLRS book, there's this part, where it's shown that $$\lim_{n\to\infty}\frac{(n^b)}{(a^n)} = 0.$$ In the same chapter, it uses the aforementioned equation to prove that any logarithmic function grows slower than any polynomial one, thus, $$\lim_{n\to\infty}\frac{\log b^n}{ n^a}$$. It does that by substituting lgn
for n
and 2^a
for a
in the first equation. How is it allowed to substitute the terms and prove the latter equation.
Saturday, 16 June 2018
limits - Polylogarithm grows slower than polynomial proof
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