# Cardinality of Infinite Sets

1. Dec 4, 2006

### mufq15

1. The problem statement, all variables and given/known data
Prove that the union of c sets of cardinality c has cardinality c.

2. Relevant equations

3. The attempt at a solution
Well, I could look for a one-to-one and onto function... maybe mapping the union of c intervaks to the reals, or something? I know how to demonstrate that a countable union of countable sets is countable, by showing how to label them.
I'm having a hard time with this one, though.

2. Dec 5, 2006

### AKG

$$\mathbb{R}^2 = \bigcup _{r \in \mathbb{R}} (\mathbb{R} \times \{ r\} )$$

This should give you an easy way to associate a c-union of c-sets with R2. Now all you need is a bijection between R and R2.

3. Dec 5, 2006

### mufq15

Ohh, I think I finally get it! (after thinking about it for a loong while...) Infinity is hard for me to wrap my head around. Thanks a lot for your help.