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.


A class is defined as being empty if and only if it has no elements.

That is:

$\forall x: x \notin A$


$\neg \exists x: x \in A$

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.