- #1

gtfitzpatrick

- 379

- 0

## Homework Statement

consider the sequence space l

_{[tex]\infty[/tex]}(

**R**) of bounded real sequences with the sup norm. If (

**X**

^{(n)}) is sequence in l

_{[tex]\infty[/tex]}(

**R**) and

**X**[tex]\in[/tex] l

_{[tex]\infty[/tex]}(

**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?