null set

The set of numbers that contain no numbers. If there is no answer to some math problems, the answer is the null set.

A group of numbers that are the solution to an equation with no valid solutions. If the return set contains no valid answers it retuns a null set. A null set is often displayed as ∅ (or Ø) or { } for simplicity.

Also called the empty set.

One formal method for defining the null set is:

ø = the set of all x such that x is not identical with x

This relies on the Axioms of Identity and Existence completely; the Axiom of Infinity is also important indirectly. It should be noted that, unlike other formal methods, this has no problem with multi-valued logic.