Common
Quantifier (logic)
Mathematical use of "for all" and "there exists"
Quantifier (logic)
In mathematical logic, quantifiers are formal counterparts of natural-language adjectives like all, some, most, few, etc. which indicate the number of objects satisfying a given property. More precisely, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier ∀ {\displaystyle \forall } in the first-order formula ∀ x x ≥ 0 {\displaystyle \forall x\;x\geq 0} expresses that all numbers in the domain are non-negative; this formula is true for the natural numbers domain, but false for the integer domain. On the other hand, the existential quantifier ∃ {\displaystyle \exists } in the formula ∃ x x 2 − 5...
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