Split the natural numbers into three sets A, B, and C so that the sets have nothing in common, they each are countably infinite, and A U B U C = the set of natural numbers.

Question

So here's what I got
A: 2,4,6,8,10...
B:1,3,5,7,9...
C: ?

I don't know what to do for C because it cannot contain any of the number in A or B. Do I just pick a number and have in continually repeat?

Answer 1

how about:
powers of 2
powers of 3
everything else

Answer 2

or, pick numbers with different remainders when divided by 3:

3n+0: 3,6,9,12,...
3n+1: 4,7,10,13,...
3n+2: 5,8,11,14,...