Definition:Principle of Mathematical Induction

Contexts
The Principle of Mathematical Induction can be introduced in a formal development of abstract algebra or mathematical logic in various contexts, and proved from first principles in each.

Also see

 * Second Principle of Mathematical Induction: used when it is not possible to prove $\map P {k + 1}$ directly from the truth of $\map P k$, but when it is possible to prove $\map P {k + 1}$ from the assumption of the truth of $\map P n$ for all values of $n_0$ such that $n_0 \le n \le k$.


 * Equivalence of Well-Ordering Principle and Induction: this, the Second Principle of Mathematical Induction, and the Well-Ordering Principle are all logically equivalent to each other.