Teaching the course titled Theoretical Foundations of Computing always presents the problem of (re)introducing studentens to the application and use of the Principle of Mathematical Induction. This link is to one discussion that I think will be helpful to my students.
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“The Principle of Mathematical Induction is a method of proof normally used to prove that a proposition is true for all natural numbers 1,2,3,…       , although there are many variations of the basic method.  The method is particularly important in discrete mathematics, and one often sees theorems proven by induction in areas like computer science.  The technique is so intuitive and familiar that it sometimes is used without reference to its use.   For example, suppose someone tells you they are going to color the natural numbers 1,2,3, …  with some color and that the number 1 will be colored blue, and that if a given number is colored blue, then the next number will also be colored blue.  Is there any doubt in your mind that all the numbers will be colored blue?  Of course not.  This is the induction axiom.  And the good thing is you don’t have to proof it.  It is an axiom”
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