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<uk,v> --> <u,k> for all v. prove uk goes to u.
a)supposed for all v in Rn <uk,v>--> <u,v> prove {uk}-->u
b)give an example of a sequence {uk} st. <uk,v> for some vector v. but uk does not converge to u.
def of convergence.
a)since this works for all v. we can let v1={1,0,0,...} then u1 --> u. now let v2={0,1,0,0,...} then u2 --> u.
so we keep doing this and each term of uk converges to a term in u.
so by point wise convergence we have convergence.
b) I don't know how to do this part. for a) i think i got it right but i can't come up with an example.
Homework Statement
a)supposed for all v in Rn <uk,v>--> <u,v> prove {uk}-->u
b)give an example of a sequence {uk} st. <uk,v> for some vector v. but uk does not converge to u.
Homework Equations
def of convergence.
The Attempt at a Solution
a)since this works for all v. we can let v1={1,0,0,...} then u1 --> u. now let v2={0,1,0,0,...} then u2 --> u.
so we keep doing this and each term of uk converges to a term in u.
so by point wise convergence we have convergence.
b) I don't know how to do this part. for a) i think i got it right but i can't come up with an example.