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
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
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?