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

• 3 ∈ S,

• if x,y ∈ S,then x−y∈S,

• if x∈S, then 2x ∈ S,

• S contains no other element.

Use Structural Induction to write a detailed, carefully structured proof that

∀ x ∈ S, ∃ n ∈ Z, x = 3n.

What I've got is since 3 is in the set, then 2 * 3 = 6 is also in the set, 6 = 3 * 2 (n=2).

Let x = 6 and y = 3, 6-3 =3 is also in the set which is 3 * 1 = 3 (n=2).

It works on x = 12, y=6 as well. Is that the way to prove it?

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# Proving sets with structural induction

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