Real Analysis: closed sets and limit points

[Askhwhelp]

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

 

[Dick]

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

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

 

[gopher_p]

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

 

[Askhwhelp]

Since not all epilson nbhd of 7 intersects the subset other than 7 which violates the definition of limit

 

[shortydeb]

If a set has no limit points, then by definition it is closed.