In standard axiomatic set theory, by the principle of extensionality, two sets are equal if they have the same elements (that is, neither of them has an element not in the other). As a result, there can be only one set with no elements, hence the usage of "the empty set" rather than "an empty set".

citation

Wikipedia contributors. (2023, October 28). Empty set. In Wikipedia, The Free Encyclopedia. Retrieved October 31, 2023, from https://en.wikipedia.org/w/index.php?title=Empty_set&oldid=1182337108

As Jesus was walking beside the Sea of Galilee, he saw two brothers, Simon called Peter and his brother Andrew. They were casting a net into the lake, for they were fishermen. Matthew 4:18 NIV

Empty set (Wikipedia) In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.