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## Homework Statement

Let C=[tex]\bigcup[/tex]

_{n=1}

^{[tex]\infty[/tex]}C

_{n}where C

_{n}=[1/n,3-(1/n)]

a) Find C in its simplest form.

b)Give a non-monotone sequence in C converging to 0.

## Homework Equations

## The Attempt at a Solution

For part a) i get C=[0,3]. Is this correct? im not sure as to wether 0 and 3 are contained in the set though. Should it be C=(0, 3)?

As for part b) im 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.

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