# Definition:Empty Class (Class Theory)

## 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.