Let C=[tex]\bigcup[/tex]n=1[tex]\infty[/tex]Cn where Cn=[1/n,3-(1/n)]
a) Find C in its simplest form.
b)Give a non-monotone sequence in C converging to 0.
The Attempt at a Solution
For part a) i get C=[0,3]. Is this correct? I am not sure as to wether 0 and 3 are contained in the set though. Should it be C=(0, 3)?
As for part b) I am not really sure here. I thought one such sequence might be
(1, 2, 1/2, 1/3, 1/4, 1/5,...). So the tail converges to zero and the first 2 terms mean it is non-monotone.