Difference between Big-O and Little-O Notation

e∈O(g) says, essentially −

• For at least one choice of a constant l>0, ∋ a constant a such that the inequality e(x)<l⋅g(x) holds ∀x>a.

e∈o(g) says, essentially −

For every choice of a constant l>0, ∋ a constant a such that the inequality e(x)<k⋅g(x) holds ∀x>a.

e∈O(g) means that e’s asymptotic growth is no faster than g’s, whereas e∈o(g) means that e’s asymptotic growth is strictly slower than g’s. It’s like ≤ versus <.

E.g.
x2∈O(x2)
x2∉o(x2)
x2∈o(x3)