Hi all,

I'm having a spot of bother on the following question; I simply do not know where to begin. Any help would be massively appreciated.

Cheers,

Kef

http://imgur.com/e1M4u.jpg

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- Nov 3rd 2009, 09:22 AMkefSequence of intervals
Hi all,

I'm having a spot of bother on the following question; I simply do not know where to begin. Any help would be massively appreciated.

Cheers,

Kef

http://imgur.com/e1M4u.jpg - Nov 3rd 2009, 10:18 AMMauritzvdworm
assume there are two such points such that $\displaystyle p,q\in J_n$ for all n then show that these two points will be the same. it is not difficult since $\displaystyle x_n\rightarrow 0 \text{ as } n\rightarrow\infty$

you can also show that there has to be at least one point and by the previously mentioned part there can then be only one - Nov 3rd 2009, 11:12 AMkef
I see, so I should go for the proof by contradiction method? Could you start me off on how to show that the points are the same? I'm having a lot of difficulty with this one.

- Nov 3rd 2009, 11:23 AMPlato
- Nov 3rd 2009, 12:32 PMkef
Sorry, I don't quite follow...

- Nov 3rd 2009, 12:39 PMPlato
Can you prove that $\displaystyle (b_n)$ is a decreasing sequence?

Can you prove that $\displaystyle (a_n)$ is a increasing sequence?

Can you prove that $\displaystyle \left( {\forall n} \right)\left( {\forall m} \right)\left[ {a_n < b_m } \right]$?

Does that mean that both sequences converge? WHY? - Nov 4th 2009, 02:32 AMkef
Thanks a lot for the help guys, it's done now. Took me a while to understand what the question was actually asking.

Cheers.