Abstract
This chapter explores the well-ordering principle, the division algorithm and some fundamental divisibility properties. In addition, through the well-ordering principle, the chapter illustrates with an additional proof technique, the principle of mathematical induction. Interesting applications of this principle, as well as the pigeonhole principle are discussed. The division algorithm is often employed to verify the correctness of a division problem. Its proof is based on the cardinal fact that is accepted as an axiom. The Euclidean algorithm is one of the best algorithms among several procedures which are used for finding the greatest common divisor (GCD) of two positive integers. With respect to induction, the chapter states that the principle of mathematical induction (PMI) is a frequently used proof technique in both mathematics and computer science. Finally, the chapter explains algorithm correctness.
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