# liminf and limsupWatch

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#1
If n is in the set of natural numbers, and An = [ -1/n , 2 ) when n is odd, and [ -3 , 1/n ) when n is even, how do I find the limsup and liminf of An?
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3 years ago
#2
I do not think there are any purists left here ...
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3 years ago
#3
Try setting n = 2m+1 for odd and n = 2m where m is a natural number. Play around and see what you can deduce in each case.
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3 years ago
#4
They don't exist.
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3 years ago
#5
(Original post by Bruce Harrisface)
If n is in the set of natural numbers, and An = [ -1/n , 2 ) when n is odd, and [ -3 , 1/n ) when n is even, how do I find the limsup and liminf of An?
Let's take a look at the definition of liminf (and I'll leave limsup to you).

So, the first step is to work out what you get from

Then let
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3 years ago
#6
(Original post by Gregorius)
Let's take a look at the definition of liminf (and I'll leave limsup to you).

So, the first step is to work out what you get from

Then let
Far be it from me to criticise you but I'm confused: he's dealing with sets and your definition is for sequences, no? Shouldn't there be some unions and intersections floating around?
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3 years ago
#7
(Original post by atsruser)
Far be it from me to criticise you but I'm confused: he's dealing with sets and your definition is for sequences, no? Shouldn't there be some unions and intersections floating around?
Goodness, I'm dozy this morning! Apologies OP, atsruser is quite right. For liminf

then apply my previous remarks to the intersection on the right hand side.
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3 years ago
#8
(Original post by Gregorius)
Goodness, I'm dozy this morning! Apologies OP, atsruser is quite right. For liminf

then apply my previous remarks to the intersection on the right hand side.
Phew. I thought that there'd been a breakthrough at York that had shaken mathematics to its very foundations for a bit.

Still, yesterday, I wasted 15 minutes on one of those Australian A level questions by using the wrong value for - maybe this website is jinxed. I mean, it can't be *us*, can it?
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3 years ago
#9
(Original post by atsruser)
Maybe this website is jinxed. I mean, it can't be *us*, can it?
No, definitely not. Something is wrong with the balance of the universe this morning.
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