TITLE: Does there exist a set containing infinite elements, whose elements themselves are sets containing infinite elements?
QUESTION [12 upvotes]: Does there exist a set containing infinite elements, whose elements themselves are sets containing infinite elements?

I think the answer is no, there is a famous paradox for it but I'm forgetting.

REPLY [2 votes]: How about several copies of the natural numbers where one number is missing from each copy:
$$\{\mathbb{N}-\{n\}\; |\; n\in \mathbb{N}\}$$