Let's say we have the following definition of set A, and we want to define A inductively. Given the definition and basis below, what is the induction?
A = {1, 3, 7, 15, 31, …}
Basis: 1 ∈ A
Induction: ?

Question

Let's say we have the following definition of set A, and we want to define A inductively. Given the definition and basis below, what is the induction?

A = {1, 3, 7, 15, 31, …}

Basis: 1 ∈ A

Induction: ?

Accepted Answer

If x  ∈ A, then 2x + 1  ∈ A.

Answer

If x  ∈ A, then x + 2  ∈ A.

Answer

If x  ∈ A, then 3x + 1  ∈ A.

Answer

If x  ∈ A, then 3x  ∈ A.

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Let's say we have the following definition of set A, and we want to define A ind...

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