Definition:Empty Class (Class Theory)

From ProofWiki
Jump to navigation Jump to search

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