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gtfitzpatrick
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Homework Statement
(1) Prove the space [tex]\ell_\infty[/tex] is complete
(2)In [tex]\ell_\infty[/tex](R) , let Y be the subspace of all sequences with only finitely many non-0 terms. Prove that Y is not complete.
The Attempt at a Solution
(1)I can show that [tex]\ell\infty[/tex] is complete by taking an arbitrary cauchy sequence and showing that xn[tex]\rightarrow[/tex] x
(2)Im not sure how to go about this.I figure the best wat to show that its not complete is to try to prove that it is complete?but I am not sure where to start?