FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Math » Undergraduate
Density of a certain set.
Post new topic   Reply to topic Page 1 of 1 [2 Posts] View previous topic :: View next topic
Author Message
Sagar Kolte
science forum beginner


Joined: 14 Apr 2005
Posts: 31

PostPosted: Thu Jun 22, 2006 4:27 pm    Post subject: Density of a certain set. Reply with quote

let 'a' be an irrational number.

consider the set {n*a|n is a natrual number}

prove that the set {x|x= n*a - [n*a]} is dense in [0 1].

note: [y]=gratest integer less than or equal to y.

Thank You.
Back to top
David C. Ullrich
science forum Guru


Joined: 28 Apr 2005
Posts: 2250

PostPosted: Fri Jun 23, 2006 10:58 am    Post subject: Re: Density of a certain set. Reply with quote

On Thu, 22 Jun 2006 12:27:37 EDT, koltesagar <sagar.kolte@gmail.com>
wrote:

Quote:
let 'a' be an irrational number.

consider the set {n*a|n is a natrual number}

prove that the set {x|x= n*a - [n*a]} is dense in [0 1].

note: [y]=gratest integer less than or equal to y.

There are interesting ways to do this using Fourier
series... A hint for an elementary solution:

Let x_n = n*a - [n*a].

The fact that a is irrational shows that the x_n are
distinct: x_n <> x_m if n <> m. (<> means "is not equal to").

Let eps > 0. Since the x_n are infinitely many elements of
[0,1) there must exist n,m with n <> m such that

|x_n - x_m| < eps.

Now...

Quote:
Thank You.


************************

David C. Ullrich
Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 1 of 1 [2 Posts] View previous topic :: View next topic
The time now is Sun Oct 23, 2011 6:45 am | All times are GMT
Forum index » Science and Technology » Math » Undergraduate
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts Density operator in second quantization erite423@yahoo.se Research 4 Mon Jul 10, 2006 3:41 pm
No new posts Is this a Time Dilation: Motion and Clocks also slow down... guskz@hotmail.com Relativity 4 Sun Jun 11, 2006 6:38 am
No new posts Clifford Algebra and Density Matrices CarlB Research 0 Thu Jun 08, 2006 8:06 am
No new posts density loss in 1d-advection.Why? coarse mesh? velocity f... Alessandro num-analysis 5 Mon May 29, 2006 2:15 pm
No new posts Question about the energy density of hydrogen fuel cells. Robert Clark Chem 7 Mon May 29, 2006 9:48 am

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.3435s ][ Queries: 16 (0.3182s) ][ GZIP on - Debug on ]