Suppose and are pointsets of . If and both have a leftmost point, prove that the union also has a leftmost point.
I can kind of see how this would be true, but I am having a lot of trouble formalizing a proof. If someone could help me along that would be great. I have just started this course, and it's a little difficult to get used to.
I'm slightly confused... I know what you're saying, but I can't see the rest of the proof... I mean, I could suppose that and that would make the left most point, or I could say the opposite, and would be the left most point. I feel like I'm missing something.
Ok...
Note: If , then . In any of these cases, either or is the left most point.
We know:
Let , then they are the same point, and that point is the left most point, since it is also the left most point of both and .
Let , then and , . In other words, it means that is to the left of all points in , and is therefore the left most point of the union.
Let , then and , . In other words, it means is to the left of all points in , and is therefore the left most point of the union.