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 the 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.
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