Transitive Class/Examples
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Examples of Transitive Classes
Empty Class
The empty class is transitive.
Singleton of Empty Class
Let $\O$ denote the empty class.
Then the singleton $\set \O$ is transitive.
Class $\set {\O, \set \O}$
Let $\O$ denote the empty class.
Then the class:
- $\set {\O, \set \O}$
is transitive.
Class $\set {\O, \set \O, \set {\O, \set \O} }$
Let $\O$ denote the empty class.
Consider the ordinal $3$, defined as:
- $\mathcal 3 := \set {\O, \set \O, \set {\O, \set \O} }$
$\mathcal 3$ is transitive.
Class $\set {\O, \set {\O, \set \O} }$
Let $\O$ denote the empty class.
Consider the class $S$, defined as:
- $S := \set {\O, \set {\O, \set \O} }$
$S$ is not transitive.
Singleton of Singleton of Empty Class is not Transitive
Let $\O$ denote the empty set.
Consider the class $S$, defined as:
- $S := \set {\set \O}$
$S$ is not transitive.