1. The problem statement, all variables and given/known data Produce an infinite collection of sets A1, A2, A3.... with the property that every Ai has an infinite number of elements, Ai∩Aj = ∅ for all i ≠ j, and the union of all Ai is equal to N. 2. Relevant equations None provided. 3. The attempt at a solution What I've come up with is that each Ai is the set of all natural numbers x with the properties that: 1.) The ith digit of x is i and 2.) x is not contained in Ai-1 It feels like it's right, but I don't know how to check, and the second criterion feels a bit cheap. Help?