Proving Non-Convergence of (X(n)) to X in l∞(R)

[gtfitzpatrick]

Homework Statement

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

Homework Equations

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.