# Thread: is this metric complete?

1. ## 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?

2. Consider this sequence:
$f_n (x) = \left\{ {\begin{array}{lr} {nx} & {0 \leqslant x \leqslant \frac{1}{n}} \\ 1 & {\frac{1}{n} < x \leqslant 1} \\
\end{array} } \right.$