The empty set is a fundamental concept in mathematics, representing a set that contains no elements. It is denoted by the symbol ∅ or by using curly braces, like this: {}. The empty set is unique, meaning there is only one empty set, and it is considered a subset of every set, including itself. In set theory, the empty set plays a crucial role in various mathematical operations and proofs. For example, when combining sets, the union of any set with the empty set results in the original set. Additionally, the intersection of any set with the empty set is always the empty set, reinforcing its identity as a set with no elements.