How can you justify the existence of an empty set?

Question

Mathematics

In set theory, such entities are only mentioned. According to G. Kantor, according to the naive set theory, an empty set cannot be defined. The empty set can only be postulated in axiomatic set theory. So in programming, before placing elements in a file, it must be created.

Answer 1

As a solution to the problem "find all real solutions to the equation sqrt (x) = -1;
The answer is "there are no such solutions", the set of solutions is an empty set.
For such situations, it was introduced.

Answer 2

In the theory of algebras, there must be zero. Those. the addition of which does not change the element. For sets, this is the empty set.