Definition 1. The universal class is the class of all sets:
\[\V = \{x : x = x\}.\]Proposition 1. $\V$ is a proper class.
Proof. Since $\V = \V$, it follows that $\V \in \V$, contrary to irreflexivity of $\in$.
Pub Mar 06, 2026 Up Jun 04, 2026
Definition 1. The universal class is the class of all sets:
\[\V = \{x : x = x\}.\]Proposition 1. $\V$ is a proper class.
Proof. Since $\V = \V$, it follows that $\V \in \V$, contrary to irreflexivity of $\in$.