(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am required to show that (C[0,1], || ||2) is a complete metric space, or to disprove that it is

2. Relevant equations

C[0,1] is the set of continuous functions on the bounded interval 0,1

3. The attempt at a solution

I am immediately confused as I am told in my notes that if every cauchy sequence from X converges then (X,d) is a complete metric space, but I find it hard to see that there clould exist a divergent cauch sequencey since cauchy sequences are all convergent right?

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# (C[0,1],|| ||2) is a complete metric space

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