(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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Prove the continuity of the norm; ie show that in any n.l.s. N if x_{n}[tex]\rightarrow[/tex] x then [tex]\left|\left|x_n\left|\left|[/tex] [tex]\rightarrow[/tex] [tex]\left|\left|x\left|\left|[/tex]

3. The attempt at a solution

i dont know where to start this

from the definition of convergence x_{n}[tex]\rightarrow[/tex] x as n[tex]\rightarrow[/tex] [tex]\infty[/tex] if [tex]\left|\left|x_n - X\left|\left|[/tex] [tex]\rightarrow[/tex] 0 as n[tex]\rightarrow[/tex] [tex]\infty[/tex]

do i use this to prove it or am i barking up the wrong tree?

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# Homework Help: Continuity of the the norm

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