Explain A function f(n)f(n) is considered O(g(n))O(g(n)), read as big oh of g(n)g(n) if there exists some positive real constant

[Learning]

Can someone please break this down for me in plain english?

A function f(n)f(n) is considered O(g(n))O(g(n)), read as big oh of g(n)g(n), if there exists some positive real constant cc and an integer n_0 > 0n
​0
​​ >0, such that the following inequality holds for all n \geq n_0n≥n
​0
​​ :

Please explain in plain english! It just seems like a bloat! i.e. all the numbers are supposed to be greater than the number n (0 or above) for it to be really called a big O. And if it really meant what I simply wrote, then it doesnt hurt for this showoff writer to write it in plain english.

thanks!

[Shinny]

Did you ever get a reply to this? I feel like the course writer didn’t understand it themselves well enough to teach it.