A) Show that $\displaystyle N$ contains infinitely many pairwise disjoint infinite subsets. [Hint: It was shown that $\displaystyle N$~$\displaystyle N$x$\displaystyle N$

what is a pairwise disjoint infinite subset, can someone provide the definition of it?

B) Prove that any infinite set can be written as the countably infinite union of pairwise disjoint infinite subsets.