How to Give a Recursive Formula for Sets of Numbers

[Goldenwind]

[SOLVED] Giving a Recursive Formula

Homework Statement

Give a recursive definition of
a) the set of odd positive integers.
b) the set of positive integer powers of 3.
c) the set of polynomials with integer coefficients.

I've solved a).
Having trouble with b).
Unsure what c) is asking.

For a), got: f(0) = 1, and f(n) = f(n – 1) + 2.

 

[Gib Z]

For b), I'm sure you could tell me what f(0) is? f(1) would be how many times f(0)? What if you repeat this process?

 

[Goldenwind]

Ahhh, now that I've slept, I see I misread the question.
It is saying 3^n, not n^3.

This makes it much easier. For n^3, I'd have to cuberoot, add 1, and cube to get to the next step, which felt like "cheating", for some reason. 3^n will be much easier.

Still unclear on what c) is referring to.