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October 18th, 2016, 06:27 PM   #1
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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.
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October 18th, 2016, 07:46 PM   #2
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Can you give some context?
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October 18th, 2016, 07:50 PM   #3
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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.
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October 18th, 2016, 07:54 PM   #4
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${0}$ 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 $A_n = (-\frac1n,0]$
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October 18th, 2016, 07:55 PM   #5
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Very good, I never think about going from the other direction. Now, there is no doubt.
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October 18th, 2016, 08:11 PM   #6
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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.
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October 19th, 2016, 02:57 AM   #7
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Can you type out the complete question?
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October 19th, 2016, 07:28 AM   #8
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$\displaystyle \lim_{n\rightarrow \infty}$ (0,1/n] = (0,0] which is all x st 0<x$\displaystyle \leq$0, which is nothing.
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October 19th, 2016, 04:37 PM   #9
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Quote:
Originally Posted by greg1313 View Post
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.
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October 20th, 2016, 01:16 PM   #10
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Anybody?
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