Consider the set T defined recursively as follows:(adsbygoogle = window.adsbygoogle || []).push({});

• 2∈T,

• if x∈T and x>1,then x/2 ∈T,

• if x∈T and x>1,then x^2 ∈T,

• T contains no other element.

Use Structural Induction to write a detailed, carefully structured proof that ∀ x ∈ T, ∃ n ∈ N, x = 2n.

I'm not sure how to do this proof.

I assume ∀ x ∈ T, ∃ n ∈ N, x = 2n is true and try to prove then x/2 ∈T and x^2 ∈T?

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# Structural Induction on Sets

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