Class is Not Element of Itself
Jump to navigation
Jump to search
Theorem
Let $A$ be a class.
Then $A$ is not an element of itself:
- $A \notin A$
Proof
$A \in A$ would create a relational loop for the class membership sign.
By No Membership Loops, this is a contradiction.
$\blacksquare$
Sources
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 5.21$