Union of two points So the union of two sets is just a set that included all the elements from them but what happens for two points?
For example, the set $X = [1,2] \cup [3,4]$.
What would be considered in this set?
 A: Assuming, though, that you mean $\lbrace (1,2) \rbrace \cup \lbrace (3,4) \rbrace$, the answer is simply the set containing both points, that is, $\lbrace (1, 2), (3,4) \rbrace$.  As you can see, it has just the two elements--no others.
A: Strictly speaking, there is a type mismatch here. You can't apply a set operation to something is not a set. Just like there is no meaning for writing $e^{\sqrt{\{0,1\}}}$, since we can't take square roots of sets and we can't raise $e$ to the power of a set.
Points are not sets, so there's no sense in talking about the union of two points.
But even more strictly, one can model everything as sets. This means that points can be thought of as sets as well. This will be similar as to how all matter is protons, electrons and neutrons. Or how all data on the computer is stored in binary code, regardless if it's an integer or a string or a complex data structure. Or how all living creatures are based on carbon: on a very fundamental level we're the same, but looking at a high level, you only share about 50% of your genes with a banana. And most of us are not yellow.
In this aspect you can take the union of two points, but the notion of a "point" is not obvious here. You can represent a point in many different way, and each way of representing the notion of a point would have different results when you take the union of two points. What is likely is that the union of two points will not result in another point, but rather in a set which does not represent a point (although you can always be a smartypants and using parlor tricks make sure that some union of points is a point).
All that being said, you can always define a notion of union of two points. This may produce another point, or it may produce a different object all together. But you will have to define it first.
A: Points cannot be taked union as a set. Only Sets can be taken.
So if $A=\{(1,2)\}$ and $B=\{(3,4)\}$, then $A\cup B=\{(1,2),(3,4)\}$.
May it helps!
