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 October 18th, 2016, 07:27 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 07:29 PM.
 October 18th, 2016, 08:46 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra Can you give some context?
 October 18th, 2016, 08:50 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, 08:54 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 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, 08:55 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, 09:11 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, 03:57 AM #7 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,981 Thanks: 1166 Math Focus: Elementary mathematics and beyond Can you type out the complete question? Thanks from ProofOfALifetime Last edited by greg1313; October 19th, 2016 at 04:18 AM.
 October 19th, 2016, 08:28 AM #8 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 $\displaystyle \lim_{n\rightarrow \infty}$ (0,1/n] = (0,0] which is all x st 0
October 19th, 2016, 05:37 PM   #9
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Quote:
 Originally Posted by greg1313 Can you type out the complete question?
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, 02:16 PM #10 Newbie   Joined: Oct 2016 From: Earth Posts: 16 Thanks: 0 Anybody?

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