# 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) eo
(ii) a|e and b|e
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
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