# Sequence space

1. Dec 9, 2009

### gtfitzpatrick

1. The problem statement, all variables and given/known data
consider the sequence space l$$\infty$$(R) of bounded real sequences with the sup norm. If (X(n)) is sequence in l$$\infty$$(R) and X $$\in$$ l$$\infty$$(R), what does it mean to say that (X(n)) converges to X

let (X(n)) be the sequence (1,1,---,1,0,0,---) with the first n coordinates 1 and the rest 0. And let x be the sequence (1) with every coordinate 1. Prove that the sequence (X(n)) does not converge to x

2. Relevant equations

3. The attempt at a solution

not sure where to start with this. any points to where i can look up info or where to start please?

2. Dec 9, 2009

### Dick

Look up the definition of the l^infinity norm. If {an} and {bn} are sequences. ||{an}-{bn}||_infinity is the sup of |an-bn| over all n.

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