### Abstract:

Over the course of this article, we will discuss irrational numbersand severaldifferent ways to prove their existence. As is commonly known, the real num-bers can be partitioned into rational numbers and irrational numbers. Rationalnumbers are those which can be represented as a ratio of two integers —i.e.,the set{ab:a, b∈Z, b6= 0}— and the irrational numbers are those whichcannot be written as the quotient of two integers. We will, in essence, showthat the set of irrational numbers is not empty. In particular, we willshow√2,e,π, andπ2are all irrational.