Hello everyone
I would like to know if there is any difference in an "analytic" pov between a limit point and a boundary point... Or answer me: ]a,b[ ... a and b are the boundary points and the limit points??
Consider the set $\displaystyle M = (0,1] \cup \left\{ 2 \right\}$.
The boundary points of $\displaystyle M$ are $\displaystyle 0,~1,~\&~2$.
But $\displaystyle 2$ is not a limit point of $\displaystyle M$.
However, any point in $\displaystyle [0,1]$ is a limit point of $\displaystyle M$.