Empty Set/Examples/Real Roots of x^2 + 1

Example of Empty Set
The set:
 * $S = \set {x \in \R: x^2 + 1 = 0}$

is an instance of a specification of the empty set.

Proof
From Existence of Real Polynomial with no Real Root, there exists no $x \in \R$ such that $x^2 + 1 = 0$.

Hence the result.