Originally Posted by **kennyb**

I have a cardinality question. If anyone can give me some guidance on this, I would greatly appreciate it. Here it goes:

If X={0,1} and w={0,1,2,...}, then show X^w and w^w have the same cardinality.

Showing that both these sets are uncountable isn't too bad, but I need them to be the same uncountable size. I'm just not seeing how to set up a bijection between these two sets. I was also thinking that I might be able to show that both sets inject into the reals, then using the continuum hypothesis. Can anyone help?