- published: 17 Mar 2016
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In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. It is denoted by the logical operator symbol ∃ (pronounced "there exists" or "for some"), which is called the existential quantifier. Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for any members of the domain.
Symbols are encoded U+2203 ∃ there exists (HTML: ∃
∃
as a mathematical symbol) and U+2204 ∄ there does not exist (HTML: ∄
).
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, and so on.
This would seem to be a logical disjunction because of the repeated use of "or". However, the "and so on" makes this impossible to integrate and to interpret as a disjunction in formal logic. Instead, the statement could be rephrased more formally as
For some natural number n, n·n = 25.
This is a single statement using existential quantification.