x Turn on thread page Beta
 You are Here: Home >< Maths

liminf and limsup watch

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?
2. I do not think there are any purists left here ...
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.
4. They don't exist.
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
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?
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.
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?
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.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 17, 2016
Today on TSR

Loughborough better than Cambridge

Loughborough at number one

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE