# Thread: Point set proof

1. ## Help with point set proof

Show that if M is a point set and there is a point p which is the first point to the right of M, then p is a limit point of M.

Definition: If M is a point set and p is a point, the statement that p is a limit point of the point set M means that every open interval containing p contains a point of M different from p.

Definition: P is the first point to the right of the point set M means that p is greater than every point of M and if q is a point less than p, then q is not greater than every point of M.

Axiom: If p and q are two distinct points then there is a point between them, for example, (p+q)/2.

2. Originally Posted by spikedpunch
Show that if M is a point set and there is a point p which is the first point to the right of M, then p is a limit point of M.
We really cannot help you unless you give us a lot more information about the axioms and definitions used in your course. If I had to guess, I would say that this is from a set of notes based on class notes given a long time ago by R L Moore or one of his students.
For example: What does the first point to the right of M mean?
If my guess is correct, then it would imply that each region that contains p must contain a point of M distinct from p. Otherwise p would not be the first point to the right of M. That is enough to make p a limit point of M.

But you see that is just a wild guess as to what the terms mean.
So you are going to have to fill a great many more details to get any meaningful help.

3. Added definitions and axiom

4. Originally Posted by spikedpunch
Added definitions and axiom
Region equals open interval.
Then the outlined proof I gave above works.