# Some Proofs of the Existence of Irrational Numbers

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 dc.contributor.author Coleman, Neal dc.date.accessioned 2020-09-03T18:54:37Z dc.date.available 2020-09-03T18:54:37Z dc.date.issued 2006 dc.identifier.citation Coleman, N. (2006). Some Proofs of the Existence of Irrational Numbers. Mathematics Exchange, 4(1), 21-25. en_US dc.identifier.uri http://cardinalscholar.bsu.edu/handle/123456789/202324 dc.description Article published in Mathematics Exchange, 4(1), 2006. en_US dc.description.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. en_US dc.title Some Proofs of the Existence of Irrational Numbers en_US dc.type Article en_US
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