Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: proof of an inequality
Replies: 12   Last Post: Apr 24, 2013 9:02 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Paul

Posts: 428
Registered: 7/12/10
Re: proof of an inequality
Posted: Apr 24, 2013 9:02 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Wednesday, April 24, 2013 11:50:46 AM UTC+1, Leon Aigret wrote:
> On Wed, 24 Apr 2013 01:04:18 -0700 (PDT), pepstein5@gmail.com wrote:
>
>
>

> >On Wednesday, April 24, 2013 1:00:13 AM UTC+1, Virgil wrote:
>
> >> In article <ken.pledger-C04AB8.09445924042013@news.eternal-september.org>,
>
> >> Ken Pledger <ken.pledger@vuw.ac.nz> wrote:
>
> >>
>
> >> > In article <ee54f5fc-33a5-4c57-8b8e-cfcf32f7f585@googlegroups.com>,
>
> >> > oercim <oercim@yahoo.com> wrote:
>
> >> >
>
> >> > > ....
>
> >> > > x1^2+x2^2+....+xn^2>=ave(x)^2
>
> >> > >
>
> >> > > does this inequality always hold? ....
>
> >>
>
> >> x^2 + y^2 >= ((x+y)/2)^2
>
> >>
>
> >
>
> >It's simpler than anyone else on this thread seems to realise. You don't need to use properties of squaring -- squaring can be replaced by any symmetric function that increases on the positive x axis.
>
> >
>
> >LHS = (abs(x1))^2 + ... (abs(xn))^2 >= (max(abs(xi))) ^ 2 >= (mean(abs(xi))) ^ 2.
>
> > ...
>
>
>
> That looks a bit strange. An other reason why it is simple is because
>
> the inequalty is just a somewhat disguised version of Cauchy-Schwarz
>
> for the 'inner product' of (x1, ... , xn) and (1, ... , 1).
>
>
>
> Leon


The OP probably means the average of x ^ 2. Under this interpretation, yours is the best way of seeing it.

Paul



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.