N refers to the set of all natural numbers.
Part 2: From the previous problem, we have σn : N → N for all n ε N.
Show that for any n ε N, σ(n+1)(N) is a subset of σn(N), where we have
used n + 1 for σ(n) as we defined in class.
2. The attempt at a solution
For Part 2, I believe the goal would be to prove that given any x ε σ(n+1)(N), that x ε σn(N) as well. For this problem, I am not sure where to start for this problem, since it seems like it would be the opposite direction (the subset would be the other way). Would knowing what the definition of σn of (N) help (if so, how is this defined/how do I work with this?)?
Figured out part 1.