Existential quantification

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 turned E (∃) logical operator symbol, which, when used together with a predicate variable, is called an existential quantifier ("∃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.

Symbols are encoded U+2203 ∃ THERE EXISTS (HTML ∃ · ∃ · as a mathematical symbol) and U+2204 ∄ THERE DOES NOT EXIST (HTML ∄).

Basics

Consider a formula that states that some natural number multiplied by itself is 25.

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