Singleton of Empty Class is Transitive

Example of Transitive Class

Let $\O$ denote the empty class.

Then the singleton $\set \O$ is transitive.


Proof

There is one element of $\set \O$, and that is $\O$.

This is a subclass of $\set \O$.

That is, $\set \O$ is transitive.

$\blacksquare$


Sources

  • 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 10$ Some useful facts about transitivity
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