Definition Notation "Little-O" ( Small O)

Question

I would like to understand a little better about Little-O Notation, it is for academic purposes, however I have not found enough content or in a somewhat "clear" way, for understanding. I’m a little lost in relation due to lack of study material.

Answer 1

Note: I will use the letter o (minuscula) for little-o; and O (capital letters) for big-O

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We say a function f is contained in o(g) if for all x it is true that f(x) < g(x).

We say a function f is contained in O(g) if for all x it is true that f(x) <= g(x).

For example, consider the function f(x) = x^2

• f is in o(x^3) and in O(x^3)
• f nay is o(x^2) nor in O(x)

Note that if f is contained in o(g) then necessarily you will be in O(g) also.