Natural numbers/Proofs/Induction principle/Fact

Mathematical induction

Suppose that for every natural number ${}n$ a statement ${}A(n)$ is given. Suppose further that the following conditions are fulfilled.

1. ${}A(0)$ is true.
2. For all ${}n$ we have: if ${}A(n)$ holds, then also ${}A(n+1)$ holds.

Then ${}A(n)$ holds for all ${}n$.

Write a proof 2, Write another proof