Singleton Class/Examples/Empty Set
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Example of Singleton Class
The singleton class $\set \O$ is the class whose only element is the empty set $\O$.
Warning
It is important to distinguish between an element, for example $a$, and a singleton containing it, that is, $\set a$.
That is $a$ and $\set a$ are not the same thing.
While it is true that:
- $a \in \set a$
it is not true that:
- $a = \set a$
neither is it true that:
- $a \in a$
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: $\S 4$ The pairing axiom