# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sat, 25 May 2013 22:26:13 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 6 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Does {1/n} n=1 to infinity converge? Why or why not?Posted: Sun, 1 Apr 2012 20:57:19 UTC
 Member

Joined: Mon, 13 Feb 2012 01:07:16 UTC
Posts: 23
hi,

Let T be the collection of all U subset R such that U is open using the usual
metric on R.Then (R; T ) is a topological space. The topology T could also be described as
all subsets U of R such that using the usual metric on R, R \ U is closed and
bounded.

Does {1/n} n=1 to infinity converge? Why or why not?

I think it does converge...it converges to 1 for example...am I right?

Does {n} n=1 to infinity converge? Why or why not?

I dont think that this sequence converges in a topological space?

thanks

Top

 Post subject: Re: Does {1/n} n=1 to infinity converge? Why or why not?Posted: Sun, 1 Apr 2012 21:19:09 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
math25 wrote:
hi,

Let T be the collection of all U subset R such that U is open using the usual
metric on R.Then (R; T ) is a topological space. The topology T could also be described as
all subsets U of R such that using the usual metric on R, R \ U is closed and
bounded.

This is false, you just redescribed the metric topology, and not all metric closed sets are compact.

Does {1/n} n=1 to infinity converge? Why or why not?

I think it does converge...it converges to 1 for example...am I right?

Does {n} n=1 to infinity converge? Why or why not?

I dont think that this sequence converges in a topological space?

thanks

Don't you know the definition of convergence? If not, you have no hope of solving these, and with the definition, I'm not sure what the problem is. Topologies are defined so that you understand what convergence means, so the response to your last remark is: topological spaces are where one talks about convergence, if you say "it doesn't converge in a topological space" you're saying "it doesn't converge in the only context where it makes sense to talk about convergence."

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Does {1/n} n=1 to infinity converge? Why or why not?Posted: Sun, 1 Apr 2012 21:43:12 UTC
 Member

Joined: Mon, 13 Feb 2012 01:07:16 UTC
Posts: 23
I 'm sorry, I meant to say that "it does not converge in usual topology on R^n"

Top

 Post subject: Re: Does {1/n} n=1 to infinity converge? Why or why not?Posted: Sun, 1 Apr 2012 21:55:22 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
math25 wrote:
I 'm sorry, I meant to say that "it does not converge in usual topology on R^n"

Yes, that is true because the sequence is not Cauchy.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Does {1/n} n=1 to infinity converge? Why or why not?Posted: Mon, 2 Apr 2012 02:18:54 UTC
 Member

Joined: Mon, 13 Feb 2012 01:07:16 UTC
Posts: 23
Also, for the first sequence I meant to say it converges to 0 not 1 in usual topology.

Top

 Post subject: Re: Does {1/n} n=1 to infinity converge? Why or why not?Posted: Mon, 2 Apr 2012 02:27:37 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
math25 wrote:
Also, for the first sequence I meant to say it converges to 0 not 1 in usual topology.

This is accurate.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 6 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

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

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous