Definition:Empty Set/Notation

Notation for the Empty Set
The symbols $\O$ and $\emptyset$ used for the empty set are properly considered as stylings of $0$ (zero), and not variants of the Greek Phi: $\Phi, \phi, \varphi$.

Despite this, some sources call the symbol phi (pronounced fie).

Some sources maintain that it is a variant on the Norwegian / Danish / Faeroese letter Ø.

The symbol $\O$ as presented here is a relatively new invention. Books prior to approximately $1960$ or $1970$ tend to use something less distinctive:


 * Some such sources use $\Box$ as the symbol for the empty set, but this is rare.


 * Other sources use $0$ (that is, the zero digit).


 * Yet others use $O$ (the capital letter).

None of these are recommended.

The preferred symbol on is $\O$ for its completely unambiguous interpretation and aesthetically pleasing, clean presentation.

Also note that $\set {}$ can always be used.