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hey,

I'm having some trouble with this question,

For part a) I know that in order for c_0 to be closed every sequence in c_0 must converge to a limit in c_0 but I am having trouble actually showing that formally with the use of the norm given.

Say x_n is a sequence in c_0 which converges to x then for any ε>0 there exists an N such that whenever n>N |x_n - x| < ε.

So that's just the definition for the limit of a sequence, but I'm having trouble how to use this to show that the limit x is in c_0 for every x_n in c_0.

Would anyone be able to help me out?

Thanks in advance

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# Homework Help: Show subspace of normed vector is closed under sup norm.

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