October 18th, 2016, 06:27 PM  #1 
Newbie Joined: Oct 2016 From: Earth Posts: 16 Thanks: 0  Quick question on limit of interval
Hi, is limit of the interval (0, 1/n] as n tends to infinity the point 0, i.e. {0} or totally nothing? I personally think it is 0 but 1/n gets closer and closer to 0 but does not actually touch 0 so I am afraid that I am wrong. I want to make sure. Thanks.
Last edited by geniusacamel; October 18th, 2016 at 06:29 PM. 
October 18th, 2016, 07:46 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,540 Thanks: 2146 Math Focus: Mainly analysis and algebra 
Can you give some context?

October 18th, 2016, 07:50 PM  #3 
Newbie Joined: Oct 2016 From: Earth Posts: 16 Thanks: 0 
My problem is to write {0} explicitly as a monotone limit of elements, A_n in I where I is of the form (a,b]. I want to check if my answer A_n = (0,1/n] is correct because I am not sure whether limit of this is the 0 point itself or totally nothing.

October 18th, 2016, 07:54 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,540 Thanks: 2146 Math Focus: Mainly analysis and algebra 
${0}$ is not in any of the sets, so it's not in the limit either. That's my opinion anyway. I would do something like $A_n = (\frac1n,0]$ 
October 18th, 2016, 07:55 PM  #5 
Newbie Joined: Oct 2016 From: Earth Posts: 16 Thanks: 0 
Very good, I never think about going from the other direction. Now, there is no doubt. 
October 18th, 2016, 08:11 PM  #6 
Newbie Joined: Oct 2016 From: Earth Posts: 16 Thanks: 0 
Anyway, do you know what does R bar (R with a a horizontal line on top) mean? I know R itself means real number. Because a and b are elements of R bar.

October 19th, 2016, 02:57 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,435 Thanks: 870 Math Focus: Elementary mathematics and beyond 
Can you type out the complete question?
Last edited by greg1313; October 19th, 2016 at 03:18 AM. 
October 19th, 2016, 07:28 AM  #8 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 965 Thanks: 78 
$\displaystyle \lim_{n\rightarrow \infty}$ (0,1/n] = (0,0] which is all x st 0<x$\displaystyle \leq$0, which is nothing.

October 19th, 2016, 04:37 PM  #9 
Newbie Joined: Oct 2016 From: Earth Posts: 16 Thanks: 0  My problem is to write {0} explicitly as a monotone limit of elements, A_n in I where I is of the form (a,b], where a and b are elements of R bar. I all the while thought that a and b are elements of R (i.e. I did not pay attention until the very last minute.) and I did not know what R bar was. I know R is (infinity, infinity). I asked my professor today what R bar was and he said R bar is [infinity, infinity] or specifically R U {infinity, infinity}, where U is the union symbol. I had to hand in my work so it was too late to change my answer if it was not valid but from what I see, (1/n, 0] is still valid because they are elements of R bar. But I am afraid that I am missing something because if this is the case, what for he need to use R bar when just R will suffice. 
October 20th, 2016, 01:16 PM  #10 
Newbie Joined: Oct 2016 From: Earth Posts: 16 Thanks: 0 
Anybody?


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interval, limit, question, quick 
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