# MACM 101 Lecture Notes - Lecture 14: Well-Ordering Principle, Short Circuit

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13 Aug 2016

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Modify the following if statement so it takes advantage of "short circuit evaluation"

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Note: short-circuit evaluation is an application of the domination law

Two last number theory definitions:

Definition:

lcm(a,b) = e when:

(i) e≥o

(ii) a|e and b|e

(iii) if a|m and b|m then e|m

Lcm(a,b) is by the least common multiple of a and b

Useful for finding common denominators

Identity: a*b = gcd(a,b) * lcm(a,b)

Well ordering principle

Every nonempty set of nonnegative integers has a smallest element

The Well Ordering Principle is an axiom and therefore there is no proof. An axiom is a fundamental

building block, upon which all other mathematics is based. It is therefore given to be true, not proven.

We could use the WOP (Well Ordering Principle) to prove the Division Algorithm and we will use the

WOP to prove the Principle of Mathematical Induction.

Lecture 14

February 5, 2016

10:33 AM

Lecture Notes Page 1