- #1

PingPong

- 62

- 0

## Homework Statement

Let [tex]A=\{(a_\alpha,b_\alpha),\alpha\in I\}[/tex] be a family of mutually non-intersecting intervals on the real line. Here [tex]I[/tex] is an arbitrary set of indexes. Prove that this family contains at most countably many elements (intervals).

## Homework Equations

None, other than all of the stuff on countability of a set.

## The Attempt at a Solution

I've tried to find an enumeration but I haven't gotten anywhere. I'm guessing that this is a property of the real line - it can only be split up into a countable number of open intervals, but I can't see how to prove it. A hint to start may be all I need.

At least I've been able to get the other five problems on this homework :)