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 Post subject: A strong inequality
PostPosted: Thu, 11 Jun 2009 22:39:37 UTC 

Joined: Sun, 23 Mar 2008 10:55:47 UTC
Posts: 29
Prove that


 Post subject: Re: A strong inequality
PostPosted: Fri, 12 Jun 2009 07:35:49 UTC 
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7624
Location: NCTS/TPE, Taiwan
mathemagics wrote:
Prove that


Rearrange, so it suffices to show 3>e-log(1-(e-1)/e^2). Then it is just a matter of using enough terms in the series expansion (e.g. taking 7 terms approximation for e and log) so the remainder term doesn't matter.

Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4

 Post subject:
PostPosted: Fri, 12 Jun 2009 13:20:06 UTC 
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Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9961
I really want to use Bernoulli's inequality somehow...

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