A) Show that contains infinitely many pairwise disjoint infinite subsets. [Hint: It was shown that ~ x
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.
for B) if S is an infinite set, we have 2 cases, S can be uncountable or countably infinite, if S uncountable, this is not possible, so we need to show that S is countable
since S is infinite, then we have , f is injective, so if we show that f is also a surjection, we have f is a bijectiion, i.e. . i.e we need to show that for all there exisis
If we have f is a bijection, then by part A, we have part B
so how can I do this?