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Im working on this equation: suppose S is the set of numbers recursively defined by:

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1∈S

x∈S→3x∈S

x∈S→x2∈S.


Use structural induction to prove that all members of S are powers of 3.

Here, by a power of 3, we mean a number of the form 3k where k

is a non-negative integer. Do not confuse "power of 3" with "multiple of 3"

and make sure to review the laws of exponentiation for this problem.

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