Mathematical Induction

Mathematical induction is a method of mathematical prooftypically used to establish that a given statement istrueof all natural numbers. It is done by proving that thefirst statement in the infinite sequence of statements istrue, and then proving that if any one statement in theinfinite sequence of statements is true, then so isthe nextone. The method can be extended to prove statements aboutmore general well-founded structures, such as trees; thisgeneralization, known as structural induction, isused inmathematical logic and computer science.