Russell’s Paradox and Possible Solutions

ABSTRACT: The beginnings of set theory as a mathematical discipline can be traced back to the work of Georg Cantor. Around 1900 when the ideas of Cantor were finally being accepted, a series of logical contradictions were found to exist in the theory of sets. The most famous of these contradictions, discovered by Bertrand Russell and known as "Russell’s Paradox," caused much worry amongst mathematicians. Russell attempted to patch this logical fallacy, but the most accepted solution today is that of Zermelo and Fraenkel. A new real world example of Russell’s paradox is examined and the solution of Zermelo and Fraenkel is applied. The origins of set theory can be traced back to a Bohemian priest, Bernhard Bolzano (1781-1848), who was a professor of religion at the University of Prague. Bolzano’s paper, Paradoxien des Unendlichen (Paradoxes of the Infinite), is the first to introduce the term set. This paper discusses the relationship between the set of natural numbers and their perfect

ABSTRACT: The beginnings of set theory as a mathematical discipline can be traced back to the work of Georg Cantor. Around 1900 when the ideas of Cantor were finally being accepted, a series of logical contradictions were found to exist in the theory of sets. The most famous of these contradictions, discovered by Bertrand Russell and known as "Russell’s Paradox," caused much worry amongst mathematicians. Russell attempted to patch this logical fallacy, but the most accepted solution today is that of Zermelo and Fraenkel. A new real world example of Russell’s paradox is examined and the solutio