Question: Suppose the sequence \(\left(f_{n}\right)\) converges uniformly to \(f\) on the set \(A\), and suppose that each \(f_{n}\) is bounded on \(A\). (That is, for each \(n\) there is a constant \(M_{n}\) such that \(\left|f_{n}(x)\right| \leq M_{n}\) for all \(x \in A\).) Show that the function \(f\) is bounded on \(A\).

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