An unusually easy proof of vector.

Thread starter athrun200
Start date Sep 18, 2011
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Proof Vector

AI Thread Summary

The discussion revolves around a proof related to the infinity norm of a vector. Participants express uncertainty about the simplicity of the proof, with one noting that the infinity norm is defined as the largest component of the vector, not just the nth component. A suggestion is made to clarify the relationship by stating that the infinity norm is less than or equal to the absolute value of the nth component. The conversation highlights the need for precision in mathematical definitions and proofs. Overall, the participants are focused on ensuring the correctness of the proof in question.

Sep 18, 2011

athrun200

Homework Statement

See the attachment.

Homework Equations

The Attempt at a Solution

It seems this proof is trivial, too easy that I am not sure if I do it correctly.

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Sep 18, 2011

HallsofIvy

Science Advisor

Homework Helper

Yes, it is too trivial

You start by saying ||u||_\infty= |u_n|. You can't do that ||u||_\infty is the largest component, not necessarily the nth component

You can say ||u||_\infty\le |u_n|. Does that help?

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