Classes

Overview

The Zermelo-Fraenkel alternative avoids speaking of collections defined using set theoretical notation that are not sets. The von Neumann-Bernays alternative calls these classes.

Russell’s Paradox

Let $R=\{x\mid x\notin x\}$. Then $R\in R\iff R\notin R$.

Bibliography

• Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
• “Russell’s Paradox,” in Wikipedia, April 18, 2024, https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437.