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

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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.*

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.

- https://www.cheenta.com/complex-number-isi-entrance-b-stat-hons-2003-problem-5/
- https://www.youtube.com/watch?v=P4ZYA4XCQoM&list=PLTDTcDkWcXuxeaAMvWpx4vGIul38dKOQp&index=4

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