Give an example of a sequence $\displaystyle \{f_{n}\} , n=1,2, ,, \infty$ of continuous functions $\displaystyle f_{n}:I \rightarrow I$ such that for each x in I = [0,1], $\displaystyle \{f_{n}\} , n=1,2, ,, \infty$ converges to a real number f(x), but the limit function f is not continuous.