[quote=@whizzball1]
<Snipped quote by Host>

It's not supposed to be realistic. It's just a paradox, something for mathematicians to think about. The maths book gives the question because it wants the reader to stop and think for a while about it. Although I suppose it can be expressed more mathematically. 

Consider a function f:N->N where the domain and codomain are the natural numbers, and each element in the domain is mapped to itself in the codomain. Is there a way to map the infinite elements of each of a group of infinite sets to the elements in the codomain, in addition to mapping those in the original domain, in a 1-1 manner?
[/quote]

What's the point of puzzles if they realistically make no sense on a deeper level?