Prove that the limit points of open interval $A=(2,3)$ subsets of the real numbers, are all the points of the interval $(2,3)$ including $2,3$.
This is my solution (sketch). I consider a succession $a_n=x-1/n$ where $x\in A\cup \{2,3\}$, $a_n$ converges to $x$ for each $x$ in A. Then each $x$ in A is limit point for A.
What do you think about my solution? Thanks.