sequence space

[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?

[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.