Definition:Empty Set

The empty set is a set which has no elements.

It is usually denoted by some variant of a zero with a line through it, for example $$\varnothing$$, and can always be represented as $$\left\{{}\right\}$$.

It is justifiable to refer to it as the empty set because there is only one empty set. That is, any two empty sets are necessarily equal, and therefore the same set.

See Empty Set Unique.

Axiomatic Set Theory
The concept of the empty set is axiomatised in the Axiom of Existence in Zermelo-Fraenkel set theory.