# Analysis Question

1. Sep 23, 2006

### barksdalemc

Guys I would appreciate any help on this. I've been trying to find an example of a collection of closed intervals of R that is uncountable. I proved that if I take a collection of open intervals of R and bijectively map them to Z, then the collection is countable, and I would assume the same with a collection of closed intervals, but clearly there must be an example where that doesnt happen and I don't understand why my logic on the collection of open sets cannot be extended to the collection of closed sets. Thanks for any help.

2. Sep 23, 2006

### StatusX

The collection { [0,a] | a$\in$A}, where A is a subset of (0,$\infty$), can be put in a bijection with A.

3. Sep 23, 2006

### barksdalemc

StatusX,

I forgot to mention the closed sets have to be disjoint.

4. Sep 23, 2006

### StatusX

Well then you could always take points as your closed intervals. It is not possible to form an uncountable set of disjoint closed intervals, each of finite length.