I have question from **Introduction to Algorithms** by CLRS,

When we say “the running time is $O(n^2),$” we mean that there is a function $f(n)$ that is $O(n^2)$ such that for any values of n, no matter what particular input of size n is chosen, the running time on the input is bounded from above by the $value:of:f(n).$

what do authors mean by saying there exits function that is $O(n^2)?$ Do they mean that this function is from the set $O(n^2).$ IS the last part which I highlighted last correct? I think it must be “…from above by the $O(n^2)$” I’ll appreciate your answers.