I am just starting to work with convex sets. I am supposed to construct a convex hull for (0,1) ∪ {2} ⊂ R.
The previous examples were pretty easy to construct since they all just consisted of points in the coordinate system. This one confuses me a little. Do I just construct it on a number line?
This is a pretty simple concept but the lesson just defined convex hull without giving examples, so I just want to make sure I am doing the right thing when moving on to more complex exercises.
I am hoping somebody could enlighten me on this.
Convex hull of a set $A$ is the smallest convex set that contains $A$.
The set $(0,1) \cup \{2\}$ it not convex currently, as it does not contains points in between $1$ and $2$. Hence we should include those points as well.
After we include those points, we obtain the set $(0,2]$. Verify that this set is convex.