Asymptotic growth of function (Comparision)

Rules for comparing asymptotic growth of functions
1)f(n) < g(n) if

2) if f(n) < g(n)  then 1/g(n) < 1/f(n)

Ordering functions according to their asymptotic growth

1) n^α < n^β 
whenever β>α
Examples
n^1.2 < n²
n^0.02 < n^0.2

2) 1 < log(log n) < log n < n^ε < n^C < n^{log n} < Cⁿ < nⁿ < C^Cn

where 0 < ε < 1 and C > 1
because  f(n)/g(n) --> infinity  as n --> infinity  for each f(n) < g(n)
Examples
n^{log n} < 2ⁿ
log n < n^0.0001
nⁿ < 2²ⁿ

3)Using the reciprocal rule in above hierarchy we can deduce that
1/n^ε < 1 / log n 
1/n^ε < 1
and so on

4) log n!  <  n log n

5)2ⁿ  <  eⁿ  <  n!  < 2²ⁿ

Reference
Concrete Mathematics, Graham Knuth Pattasnik
Algorithms, Cormen   Leiserson   Rivest