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## 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?

## 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.