S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Sun, 26 Oct 2014 00:32:23 UTC

All times are UTC [ DST ]




Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: A strong inequality
PostPosted: Thu, 11 Jun 2009 22:39:37 UTC 
Offline
Member

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

e(e-1)>e^{e-1}-1.


Top
 Profile  
 
 Post subject: Re: A strong inequality
PostPosted: Fri, 12 Jun 2009 07:35:49 UTC 
Offline
Moderator
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6946
Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
mathemagics wrote:
Prove that

e(e-1)>e^{e-1}-1.


Spoiler:
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.

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
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
\end{aligned}


Top
 Profile  
 
 Post subject:
PostPosted: Fri, 12 Jun 2009 13:20:06 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame
User avatar

Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9837
I really want to use Bernoulli's inequality somehow...


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC [ DST ]


Who is online

Users browsing this forum: No registered users


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA