Intervals and their subsets proof

[hlin818]

Homework Statement

I reduced another problem to the following problem:

If I is an interval and A is a subset of I, then A is either an interval, a set of discreet points, a union of the two.

Homework Equations

The Attempt at a Solution

Is this trivial?

 

[Office_Shredder]

It's false. For example, take the set (-1,1) and inside of it the set A of all rational numbers in between -1 and 1. Unless by union you mean any arbitrary amount of sets being unioned together, in which case it's a silly question because any set A is the union of the sets each containing a single point of A

 

[hlin818]

Ah completely overlooked that, thanks. I'll post up the full problem because now I'm sort of stuck.