Singleton

🅟 Feb 16, 2026

  🅤 Feb 22, 2026

Set Theory > Sets

DEF-SG. Singleton.

The singleton containing $a$, written as $\{a\}$, is the set $\{a,a\}$.

DEF-SG-SLF.

For any $X$,

\[X \neq \{X\}.\]

Proof.This is a consequence of Axiom of Regularlity.$\square$