I have the following question Picture of the question
What is the cardinality of $D=\{A \subseteq \Bbb N \mid \vert A \vert = \aleph_0 \land \vert \Bbb N \setminus A \vert = \aleph_0 \}$?
I do understand that A could be N even, or N odd for example But how do I find the amount of Countably infinite sets in N? I can’t think of more than just N odd and N even, but I’m not sure how to prove that they are the only countably infinite sets inside the natural numbers
Edit - I thought now and I understand I could also define A as {2, 3 ….} and so on, so there are infinite possibilities to build such set. How do I define that cardinality?