Some Proofs of the Existence of Irrational Numbers

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Show simple item record Coleman, Neal 2020-09-03T18:54:37Z 2020-09-03T18:54:37Z 2006
dc.identifier.citation Coleman, N. (2006). Some Proofs of the Existence of Irrational Numbers. Mathematics Exchange, 4(1), 21-25. en_US
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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