Definition Notation "Little-O" (Small O)

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Definition Notation "Little-O" (Small O)

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I would like to understand a little better about Little-O Notation, it's for academic purposes, but I have not found enough content or in a slightly "clearer" way, for understanding. I'm a little lost in relationship due to lack of study material.

asked by anonymous 29.08.2018 / 19:16

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Note: I'm going to use the letter o (tiny) for little-o; and O (uppercase) to big-O

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

We say that 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 no is o(x^2) nor O(x)

Note that if f is contained in o(g) then it will necessarily be in O(g) as well.