- #1
jack476
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Homework Statement
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.
Homework Equations
None provided.
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?