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## Homework Statement

{u

_{k}} is in R

^{n}and converges to u in R

^{n}

let v be in R

^{n}and v is orthogonal to each u

_{k}.

prove v is orthogonal to u

## Homework Equations

just definition of convergence. and orthogonality. <v,u>=0 if v is orthogonal to u.

## The Attempt at a Solution

u

_{k}converges so it is cauchy, so it's terms are getting closer to each other.

for epsilon>0 , there exists k>= k

_{0}st. ||u

_{k}-u|| < epsilon

so if v is orthogonal to u

_{k}then u is orthogonal to each term in u

_{k}. but the terms of u

_{k}are getting closer to u. so if v is orthogonal to a u

_{k}that is very close to u, then it is also orthogonal to u.

this proof is in no way formal but i think i have the right idea. can some one please help rewrite this?