Thread: 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.

Originally Posted by spikedpunch

Help please!
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.

Added definitions and axiom

Originally Posted by spikedpunch

Added definitions and axiom

Region equals open interval.
Then the outlined proof I gave above works.