Definition:Empty Class (Class Theory)
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This page is about Empty Class in the context of Class Theory. For other uses, see Empty Class.
Definition
A class is defined as being empty if and only if it has no elements.
That is:
- $\forall x: x \notin A$
or:
- $\neg \exists x: x \in A$
The empty class is usually denoted $\O$ or $\emptyset$.
On $\mathsf{Pr} \infty \mathsf{fWiki}$ the preferred symbol is $\O$.
Also see
- Results about the empty class can be found here.
Technical Note
The $\LaTeX$ code for \(\O\) is \O
.
The same symbol is also generated by \varnothing
or \empty
, but these are more unwieldy, and \O
is preferred.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): empty: 1.
- 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: $\S 3$ Axiom of the empty set