Cos(x) is not closed function?

1. Mar 29, 2010

emptyboat

I think cos(x) is closed function in R.
But I heard that cos(x) is not closed function in R.
What do I choose closed set A in R, cos(A) is not closed in R?
Help....

2. Mar 29, 2010

quasar987

Consider for instance the set $A := \{2n\pi-1/n: n\in\mathbb{N}\}$. It is closed, but cos(A) does not contain its limit point 1.

3. Mar 29, 2010

emptyboat

Thank you, friend. I tried closed intervals...