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## Homework Statement

N refers to the set of all natural numbers.

Part 2: From the previous problem, we have σ

^{n}: N → N for all n ε N.

Show that for any n ε N, σ

^{(n+1)}(N) is a subset of σ

^{n}(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 σ

^{n}(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 σ

^{n}of (N) help (if so, how is this defined/how do I work with this?)?

Figured out part 1.

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