Describe a partition of $\mathbb{N}$ that divides $\mathbb{N}$ into $\aleph_0$ countably infinite subsets.

Question

Does anyone have any hints on how to describe the following partition?

Describe a partition of $\mathbb{N}$ that divides $\mathbb{N}$ into $\aleph_0$ countably infinite subsets.

Powers of $2$, powers of $3$,powers of $5$, ..., numbers that aren't powers of a prime. — lulu, Oct 28 '16 at 20:38

score 0 · Answer 1 · answered Oct 28 '16 at 20:38

0

Hint:

How many numbers are coprime to $2$? How many numbers have exactly one factor of $2$? How many numbers have exactly two factors of $2$? $\dots$

answered Oct 28 '16 at 20:38

JMoravitz

1 Answers1