What is Functional Analysis and How Can It Be Applied in Science?

[math8]

See the attachment.

 

[Dick]

I really don't think there is much to show. How do you define an infinite sum like the sum of x_k*e_k? I would say it's the sequence whose i-th term is the sum of the i-ith terms of all of the x_k*e_k. So for a given i there's only one sequence with a nonzero term. You definitely don't want to start trying to prove the partial sums converge in the l_infinity norm. They don't unless x converges to zero (in the real infinite sequence sense).

 

[maze]

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