if you follow the view of constructive mathematics then a collection of numbers is subcountable if there is a partial surjection from the natural numbers onto it(or that a collection is no bigger than the counting numbers) so the answer could be c depending on your stance
I think in this case, you need the bijection function (not the surjection function). You can represent an infinite amount of irrational numbers between 0 and 1 by using infinite strings of just 1s and 0s while you can represent the natural numbers as 1,2,3,~
Using Cantor's diagonalization, you will generate a particular number that will not be able to pair up with another rational number so long as they go out infinitely long (which makes creating a bijection impossible)
Day[9] probably explained it much better here: Link
[Edited by Neo7, 10/11/2011 11:14:13 AM]