existential quantification
Sign in to saveAlso known as exist, exists, there exists, there exists at least one, ∃, for some, for one or more, there exists one or more
logical quantification stating that a statement holds for at least one object
Key facts
- Type
- Quantifier
- Field
- Mathematical logic
- Statement
- ∃ x P ( x ) {\displaystyle \exists xP(x)} is true when P ( x ) {\displaystyle P(x)} is true for at least one value of x {\displaystyle x} .
- Symbolic statement
- ∃ x P ( x ) {\displaystyle \exists xP(x)}
via Wikipedia infobox
~10 min read
Encyclopedic overview
In predicate logic, an existential quantification is a type of quantifier which asserts the existence of an object with a given property. 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)"), read as "there exists", "there is at least one", or "for some". 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.
Quantification in general is covered in the article on quantification (logic). The existential quantifier is encoded as U+2203 ∃ THERE EXISTS in Unicode, and as \exists in LaTeX and related formula editors.
Excerpted from Wikipedia’s “existential quantification” article, available under the CC BY-SA 4.0 licence.