Cos(x) is not closed function?

  • Thread starter emptyboat
  • Start date
  • #1
emptyboat
28
1
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....
 

Answers and Replies

  • #2
quasar987
Science Advisor
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Consider for instance the set [itex]A := \{2n\pi-1/n: n\in\mathbb{N}\}[/itex]. It is closed, but cos(A) does not contain its limit point 1.
 
  • #3
emptyboat
28
1
Thank you, friend. I tried closed intervals...
 

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