常用数学术语和符号.

Asymptotic notation 渐进符号

Θ-notation  -  Asymptotic tight bound
读法：Θ(n²)  - pronounced "theta of n-squared".
意义：For a given function g(n), we denote by Θ(g(n)) the set of functions

Θ(g(n)) = {f(n) : there exist positive constants c₁, c₂, and n₀ such that 0 ≤ c₁g(n) ≤ f(n) ≤ c₂g(n) for all n ≥ n₀}.
(Within set notation, a colon should be read as "such that.")

O-notation - Asymptotic upper bound
读法：O(g(n)) - pronounced "big-oh of g of n" or sometimes just "oh of g of n".
意义：For a given function g(n), we denote by O(g(n)) the set of functions

O(g(n)) = {f(n): there exist positive constants c and n₀ such that 0 ≤ f(n) ≤ cg(n) for all n ≥ n₀}.

Ω-notation - Asymptotic lower bound
读法：Ω(g(n)) - pronounced "big-omega of g of n" or sometimes just "omega of g of n")
意义：For a given function g(n), we denote by Ω(g(n))  the set of functions

Ω(g(n)) = {f(n): there exist positive constants c and n₀ such that 0 ≤ cg(n) ≤ f(n) for all n ≥ n₀}.

Monotonicity 单调性

A function f(n) is monotonically increasing if m ≤ n implies f(m) ≤ f(n).
A function f(n) is monotonically decreasing if m ≤ n implies f(m) ≥ f(n).
A function f(n) is strictly increasing if m < n implies f(m) < f(n).
A function f(n) is strictly decreasing if m < n implies f(m) > f(n).

Floors and Ceiling 底和顶

For any real number x, we denote the greatest integer less than or equal to x by ⌊x⌋ (read "the floor of x") and the least integer greater than or equal to x by ⌈x⌉ (read "the ceiling of x"). For all real x,