# Cos(x) is not closed function?

## Main Question or Discussion Point

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....

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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.