Show that if f(n) and g(n) are monotonically increasing functions, then so are the functions f(n) + g(n) and f (g(n)), and if f(n) and g(n) are in addition nonnegative, then f(n) · g(n) is monotonically increasing.
求导即可
Prove equation (3.15).
Prove equation (3.18). Also prove that n! = ω(2^n) and n! = o(n^n).
采用暴力方法，直接证明极限在一个常数区间内
Is the function polynomially bounded? Is the function
polynomially bounded?
多项式边界也就是函数
两边取对数得到
所以，如果一个函数f(n)是有多项式边界，就满足
令
令
Which is asymptotically larger: lg(lg n)* or lg(lg n)*?
第2个大. Suppose log star of n is k, then the first one is log(k) while the second one is k - 1.
...表示多重对数函数的逆操作
Prove by induction that the ith Fibonacci number satisfies the equality
Prove that for i ≥ 0, the (i + 2)nd Fibonacci number satisfies Fi+2 ≥ φi.
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