INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

February 29, 2020

Well ordering principle and Bezout Theorem

Get motivated


Consider the following set of numbers:

$$ \displaystyle {M = \{ \frac{1}{1}, \frac{1}{2}, \frac{1}{3}, ... \} }$$

Does this set have a least number? Can you rigorously prove your answer?

Concepts in this lesson will help you to answer this question and more.

Concept - Well ordering principle, Bezout Theorem


The well-ordering principle states that every non-empty set of positive integers contains a least element.

Counter Example: The set of rational numbers does not have this property

Bezout Theorem: Let a and b be integers with greatest common divisor d. Then, there exist integers x and y such that ax + by = d. More generally, the integers of the form ax + by are exactly the multiples of d.

Watch Part 1


Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
enter