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## Homework Statement

Please just tell if I'm right or wrong on these. I think they should be fairly easy, but I don't want to say too much and end up looking like an idiot in case there is a mistake =p

We are supposed to say if it's bounded above and/or below. Also to indicate supremum and infimum if they exist

## Homework Equations

(a) [tex]{n \in Z: \cos n!}[/tex]

Not sure how to do this, but intersection runs from 1 to infinity

(b) [tex]\bigcap (\frac{1}{n},1+\frac{1}{n})[/tex]

## The Attempt at a Solution

On (a) I'm assuming that n can only be positive integers (not sure what the factorial of a negative integer means). Then it forms a subset of Reals (-1, 1) (1 and -1 are not included since factorials are not 0 or irrational) with some gaps.

Thus it's bounded above and below and supremum = 1 and infimum = -1

On (b), the intersection turns out to be just {1}. This is bounded above and below and infimum = supremum = 1.