$S = \{1,1.1,0.9,1.01,\cdots\}$

Question

$S = \{1,1.1,0.9,1.01,\cdots\}$

The following conclusions I drew from the set:

The set is bounded with $\sup S = 1.1$ and $\inf S = 0.9$, thus the bound is attained by the set.

The interior of the set is empty. The set is closed, and hence compact.

What will be the limit points of the set?

Also please verify the conclusions. Thank You.

Answer 1

All your conclusions are correct.

The only limit point of the set is $1$,since you are approaching from both sides.

All the other points are isolated points.