Give a recursive definition of the set of positive integer powers of 3.That is the set {3,9,27,81,...}

We have set A,

3 ∈ S

n*3 if n ∈ S

Explanation:

A recursion can be defined as a way of defining objects in terms of itself or as parts of itself.

Lets say we a set that is defined as A,

Then the recursive definition of the sets of positive integers with the powers of 3 in A is given as

3 ∈ S

n*3 if n ∈ S

This tells us that 3 is an element of S such that if n is an element of S then in general we would have n*3 to be an element of S