I have this homework question. Consider the set $X = \{1,2,3\}$.
$(a)$ With the natural order on $X$, find the basis for its order topology,
$(b)$ Show that the order topology on $X$ equals its discrete topology.
I suppose the natural order to be $1<2<3$, so that $1$ the is the least element and $3$ is the largest element, then $B=\{[1,3),(1,3),(1,3]\}$ is the basis for the order topology on $X$.
For part $(b)$, I would like to write $B=\bigg\{\{1,2\},\{2\},\{2,3\}\bigg\}$ but I see it will not satisfy. I need help!
Thanks.