Is $(0,2)\cup(2,3)$ dense in$ [0,3]$?

Question

I think $(0,2)\cup(2,3)$ is dense in [0,3] since the only problem point would be 2

but $B(2,r)\cup [0,3]$ is non-empty for all $r>0$

is this ok?

Answer 1

Hint: What is the closure of $(0,2)\cup (2,3)$ in $[0,3]$?