Mathematical induction is a method of mathematical proof typically used to establish a given statement for all natural numbers.

To proof the formula *A*(*n*) for all natural numbers *n* ≥ *m,* two steps are necessary:

1. the **base case**, to show that *A*(*m*) is true.

2. the **inductive step**, show that if *A*(*n*) holds, then also A(n+1) for *n* ≥ *m* holds.

Usually applies m=0 or m=1. In special cases can be m>1.

**Example: The proof of 1+2+3+…+n.**

- 2n³ + 3n² + n is divisible by 6
- The n-th derivative
- (n^p – n) is divisible by p
- The power set of a set with n elements contains 2^n elements
- Recursive Sequence
- Bernoulli’s inequality
- Just another inequality
- n and sqrt(n)
- n! > 2^n
- 2^n > n^3
- A sum
- A product
- Every integer n >= 2 is a product of prime numbers