Question

Proof By Induction - Base Case of 0

Answer 1

Depends how the natural numbers are defined. By the Peano Axioms, they do include 0. For the validity of the proof, it doesn't matter. In theory, you could use any integer as a base case and prove the statement for all integers bigger than or equal to it as long as the induction step is correct

Answer 2

The base case is performed on the first natural number. You can define the natural numbers starting at 0, but you can also define the natural numbers starting at 1.

Answer 3

What if the claim is true for n>=-1?