# Thread: Boundary pts Vs. limit pts.

1. ## Boundary pts Vs. limit pts.

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??

2. Originally Posted by rebghb
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 $\displaystyle M$.

3. okay i got that... what can we say about 2 then?? is it isolated?? and is set M bounded?? (ps im nwe to this so patience please)

4. A boundary point that is not a limit point is an isolated point.
If there is a $\displaystyle B>0$ such that $\displaystyle M\subseteq [-B,B]$ then the set is bounded.