A caracterização dos números reais por Georg Cantor

Abstract

This paper presents a translation of Georg Cantor's article "On a property of the collection of ali real algebric numbers "jirst published in 1874. ln this article Cantor enumerates the algebric numbers and realizes the impossibility of doing the sarne with real numbers. Then he finds "clear di.fference between a continum system of numbers and a system of species fonned by the set of ali real algebric numbers . Such distintion between infinite sets was basic for the development of his 'famous' theoryoftransfinite numbers, in 1895. To proceed this translation it was necessary understanding the context of the period, on mathe­matics development. Stand out the rigors definition of real numbers, wich were intuitively conceived.