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Math Help - is this metric complete?

  1. #1
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    is this metric complete?

    c[0,1] represents the set of continuous functions on [0,1]

    d(f,g)= sqrt( integral( |f-g|^2, from 0 to 1))

    is (c,d) complete? any counterexample if not?
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  2. #2
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    Consider this sequence:
    f_n (x) = \left\{ {\begin{array}{lr}    {nx} & {0 \leqslant x \leqslant \frac{1}{n}}  \\   1 & {\frac{1}{n} < x \leqslant 1}  \\<br />
 \end{array} } \right.
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