Real Analysis: closed sets and limit points

1. Nov 14, 2013

For the following example:(if possible give example or just state impossible

1) a bounded subset A of R for which sup A is not a limit point of A. An example is (0,1) union {7}. will this work?

2) a finite subset A of R that is not closed
I think it is not possible. Please give some hints if you think there is an answer

2. Nov 14, 2013

Dick

1) works fine. For 2), can you think of a proof that nobody will be able to come up with an example?

Last edited: Nov 14, 2013
3. Nov 14, 2013

gopher_p

Wait ... why is $7$ not a limit point of $(0,1)\cup\{7\}$?

4. Nov 14, 2013