Can You Prove This Complex Sequence Inequality?

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    Inequality Proof
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Discussion Overview

The discussion revolves around proving a specific inequality related to complex sequences, focusing on the mathematical formulation and potential approaches to the proof. The scope includes mathematical reasoning and exploratory discussions regarding the complexity of the problem.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the inequality involving a complex sequence and invites others to engage with the proof.
  • Another participant expresses skepticism about the complexity, suggesting that the symbols may be overly complicated.
  • A different participant acknowledges the importance of the missing part of the proof while affirming the validity of the bound.
  • Several participants express a desire for clarification or explanation regarding the inequality and its components.
  • One participant claims to know the solution but chooses not to share it to allow others the opportunity to solve it.
  • A humorous remark is made comparing the problem to "packman eating flies," suggesting a light-hearted approach to the complexity of the answer.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the clarity of the inequality or the approach to proving it. There are multiple competing views regarding the complexity and understanding of the problem.

Contextual Notes

Some participants indicate a lack of familiarity with complex numbers, which may affect their ability to engage with the proof. There are also references to missing parts of the proof that remain unresolved.

Townsend
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Show that for each complex sequence [tex]c_1, c_2, ..., c_n[/tex] and for each integer [tex]1 \leq H < N[/tex] one has the inequality

[tex] | \sum_{n=1}^N c_n|^2 \leq \frac{4N}{H+1} ( \sum_{n=1}^N |c_n|^2 + \sum_{h=1}^H | \rho_N(h)|)[/tex]

Any one...matt grime perhaps? :wink:

note: if anyone actually wants to work this out let me know and I will fill in the missing parts...but don't ask me to do it... :-p
 
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Yeah, that's good. The more fancy meaningless symbols, the better. :biggrin:
 
honestrosewater said:
Yeah, that's good. The more fancy meaningless symbols, the better. :biggrin:

There is an important part missing but it is a true bound...not just meaningless... :smile:
 
Okay, I'll take your word for it. It would be nice if someone were around to explain it to me. :wink:
 
honestrosewater said:
Okay, I'll take your word for it. It would be nice if someone were around to explain it to me. :wink:

Yeah...it would take a really smart...creative...mathematician to do so...who would be able to do that I wonder?
 
Townsend said:
Yeah...it would take a really smart...creative...
... and patient. I've never even worked with complex numbers before. You can just treat them as ordered pairs of real numbers, right? I think I'd like that approach.
 
I know the solution, but I won't say to give other people a chance. It's not that hard.
 
Its packman eating flies, so the ansewer must be MxBxHs
 

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