# Thread: inf (s) and sup (S) belong to the closure of S

1. ## inf (s) and sup (S) belong to the closure of S

,.good day,.,.ammm,.,.i need ur help to show this problem,.

If S is any bounded set of real numbers, show that the numbers inf (s) and sup (S) belong to the closure of S.

thnx,.,

2. ## Re: inf (s) and sup (S) belong to the closure of S

Originally Posted by aldrincabrera
If S is any bounded set of real numbers, show that the numbers inf (s) and sup (S) belong to the closure of S.
This follows at once if one notes that $\inf(S)$ is either a point or a limit point of $S$ .