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**N**such that xn=0,∀n≥n.

Let {e_i}, i∈

**N**be the set where e_i is the sequence in c_00 given by (e_i)_n =1 if n=i and (e_i)_n=0 if n≠i.

Show that (e_i), i∈

**N**is a basis for c_00.

So I need to show it's linearly independent and that it spans c_00. I am not sure how to go about proving this makes it confusing is that it's an infinite set, so I can't use the usual method and take a finite number of vectors.

I have an idea of how to prove linear independence, but not spanning.

Any tips/hints?

Thanks