Russell's Paradox


Consider the set S of all sets which are not members of themselves: is S a member of itself? Either answer leads to a contradiction. Russell's Paradox, as this is called, showed that Cantor's original formulation of set theory was inconsistent and led to more precise axiomatizations of set theory, such as the Zermelo-Frankl axioms.


This concept has the prerequisites:


  • Know what Russell's Paradox refers to and why it is a contradiction in naive set theory
  • Know what is meant by the (unrestricted) Axiom of Comprehension and why it is responsible for the paradox

Core resources (read/watch one of the following)


An Introduction to Set Theory (2008)
Lecture notes on axiomatic set theory.
Author: William A. R. Weiss


See also

-No Additional Notes-