The principle of mathematical induction: a product of the intuitive mind.

Abstract

Mathematical induction is prevalent in many varied areas of mathematics, and has several very necessary and useful applications. Yet induction, as a deductive method, is often not fully comprehended by the person applying it. This thesis presents mathematical induction in both a theoretical and applicational light. The reason for this is to encourage a more indepth and comprehensive understanding of mathematical induction and the theory behind it. A further purpose of this thesis, is to expose the reader to a variety of applications and variations in the principle of induction. This is done by presenting induction from the first principle to the transfinite case, and fully documenting each with the appropriate theory and examples.