How would you write an explanation of the idea behind mathematical induction for a fellow student?
Well, to show that a certain equality or inequality which depends on some whole-valued parameter, say n, is actually an identity for all the certain values of that parameter, we can often use induction.
The basic idea of induction is that we assume the equality or inequlity holds for the first possible value of n. In most cases this value is n=1, but it could be n=0, n=3 and etc. After that, we assume that the equlity or inequality holds for n=k (k is a whole nmuber) and we must prove that based on this assumption the equality or ...
Mathematical induction is explained...from a student's viewpoint.