Comparison of the asymptotic notations
Let f(n)
and g(n)
be two functions defined on the set of the positive real numbers, c, c1, c2, n0
are positive real constants.
Notation  f(n) = O(g(n))  f(n) = Ω(g(n))  f(n) = Θ(g(n))  f(n) = o(g(n))  f(n) = ω(g(n)) 
——  ——  ——  ——  ——  —— 
Formal definition  ∃ c > 0, ∃ n0 > 0 : ∀ n ≥ n0, 0 ≤ f(n) ≤ c g(n)
 ∃ c > 0, ∃ n0 > 0 : ∀ n ≥ n0, 0 ≤ c g(n) ≤ f(n)
 ∃ c1, c2 > 0, ∃ n0 > 0 : ∀ n ≥ n0, 0 ≤ c1 g(n) ≤ f(n) ≤ c2 g(n)
 ∀ c > 0, ∃ n0 > 0 : ∀ n ≥ n0, 0 ≤ f(n) < c g(n)
 ∀ c > 0, ∃ n0 > 0 : ∀ n ≥ n0, 0 ≤ c g(n) < f(n)

Analogy between the asymptotic comparison of f, g
and real numbers a, b
 a ≤ b
 a ≥ b
 a = b
 a < b
 a > b

Example  7n + 10 = O(n^2 + n  9)
 n^3  34 = Ω(10n^2  7n + 1)
 1/2 n^2  7n = Θ(n^2)
 5n^2 = o(n^3)
 7n^2 = ω(n)

Graphic interpretation      
The asymptotic notations can be represented on a Venn diagram as follows:
Links
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein. Introduction to Algorithms.