- #1
gtfitzpatrick
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Homework Statement
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Prove the continuity of the norm; ie show that in any n.l.s. N if xn [tex]\rightarrow[/tex] x then [tex]\left|\left|x_n\left|\left|[/tex] [tex]\rightarrow[/tex] [tex]\left|\left|x\left|\left|[/tex]
The Attempt at a Solution
i don't know where to start this
from the definition of convergence xn [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?