21127 Lecture Notes - Lecture 9: Mathematical Induction, Prut, Eni
16 Dec 2015
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Document Summary
Bertrand russell identi ed an issue with set theory in 1901. X = {1, 2, 3, x}, the set of all sets. Bertrand russell discovered this paradox and sent it in a letter to g. frege just as frege was completing grundlagen der arithmetik. This invalidated much of the rigor of the work, and. Frege was forced to add a note at the end stating, a scientist can hardly meet with anything more undesirable than to have the foundation give way just as the work is nished. I was put in this position by a letter from mr. bertrand russell when the work was nearly through the press. We don"t want to allow this object to be a set. We want our theory to not have such weird inconsistencies. Some xes were proposed later in 1908, by russell and ernst zermelo. This is the reason we should always specify a universal set when we use set-builder notation.
