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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Structural Induction on Sets

**Physics Forums | Science Articles, Homework Help, Discussion**