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Concept
Existential quantification
Summary
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"). Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain. Some sources use the term existentialization to refer to existential quantification.
Basics
Consider a formula that states that some natural number multiplied by itself is 25.
: 0·0 = 25, or 1·1 = 25, or 2·2 = 25, or 3·3 = 25, ...
This would seem to be a logical disjunction because of the repeated use of "or". However, the ellipses make this impossible to integrate and to interpret it as a disjunction in formal logic.
Instead, the statement could be rephrased more formall
Official source
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