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

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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.


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

Hence the result.