Full Idea
The empty set is mainly a mathematical convenience - defining a set by describing the properties of its members in an involved way, we may not know from the very beginning what its members are.
Gist of Idea
The empty set is useful for defining sets by properties, when the members are not yet known
Source
Michal Walicki (Introduction to Mathematical Logic [2012], 1.1)
Book Reference
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.45