Explain why the statement, “The running time of algorithm \(A\) is at least \(O(n^2)\),” is meaningless.

\(T(n)\) is the running time of algorithm \(A\). The statement above is saying that \(T(n) \geq O(n^2)\) which does not tell us enough to specify the upper-bound of \(T(n)\). Furthermore, even if the statement were more specific and told us that \(A = O(n^2)\) that still wouldn’t be enough to determine the lower-bound of \(T(n)\) since it could be any function that grows slower than \(n^2\). Ultimately this statement is describing an infinite set of functions and is therefore meaningless.