# algorithms – “Running time is \$O(n^2)\$” meaning

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.