Editing Universe (mathematics) (section)

==In predicate calculus==
In an [[interpretation (logic)|interpretation]] of [[first-order logic]], the universe (or domain of discourse) is the set of individuals (individual constants) over which the [[Quantifier (logic)|quantifiers]] range. A proposition such as {{math|[[Universal quantification|∀]]''x'' (''x''<sup>2</sup> ≠ 2)}} is ambiguous, if no domain of discourse has been identified.  In one interpretation, the domain of discourse could be the set of [[real number]]s; in another interpretation, it could be the set of [[natural number]]s. If the domain of discourse is the set of real numbers, the proposition is false, with {{math|1=''x'' = {{radic|2}}}} as counterexample; if the domain is the set of naturals, the proposition is true, since 2 is not the square of any natural number.