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# Cauchy Shwartz inequality proof watch

1. I'm reading a book which gives a proof of the Cauchy-Schwarz inequality. It starts by proving the following theorem (F is a general field with characteristic not 2):

If and , then there exists such that

After the proof the book reads, "For F being the field of real numbers, the above theorem gives a hilarious proof of the Cauchy-Schwarz inequality!".
I can see how the theorem proves the C/S inequality for but does it prove it for all n? Also, does anyone else find it hilarious?
2. Say we call the vectors and but . Then suppose , and extend the vectors to be of length , with .

I'm not sure how it's particularly hilarious, but it's quite cool I suppose.
3. (Original post by 0-))
After the proof the book reads, "For F being the field of real numbers, the above theorem gives a hilarious proof of the Cauchy-Schwarz inequality!"
4. (Original post by nuodai)
Say we call the vectors and but . Then suppose , and extend the vectors to be of length , with .

I'm not sure how it's particularly hilarious, but it's quite cool I suppose.
Thank you!

I now realise why it's hilarious but it's one of those jokes where you have to be there .
5. (Original post by 0-))
Thank you!

I now realise why it's hilarious but it's one of those jokes where you have to be there .
Clearly

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Updated: March 29, 2011
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