Editing Existential quantification (section)

{{Short description|Mathematical use of "there exists"}}
{{redirect2|∃&nbsp;|∄&nbsp;|the letter turned E|Ǝ|the Japanese katakana ヨ|Yo (kana)|the Ukrainian nightclub also called ∄&nbsp;|K41 (nightclub)}}
{{Infobox mathematical statement
| name = Existential quantification
| type = [[Quantification (logic)|Quantifier]]
| field = [[Mathematical logic]]
| statement = <math>\exists xP(x)</math> is true when <math>P(x)</math> is true for at least one value of <math>x</math>.
| symbolic statement = <math>\exists xP(x)</math>
}}
In [[predicate logic]], an '''existential quantification''' is a type of [[Quantifier (logic)|quantifier]], a [[logical constant]] which is [[interpretation (logic)|interpreted]] as "there exists", "there is at least one", or "for some". It is usually denoted by the [[logical connective|logical operator]] [[Symbol (formal)|symbol]] ∃, which, when used together with a predicate variable, is called an '''existential quantifier''' ("{{math|∃''x''}}" or "{{math|∃(''x'')}}" or "{{math|(∃''x'')"<ref>{{cite book |last1=Bergmann|first1=Merrie |title=The Logic Book |date=2014 |publisher=McGraw Hill|isbn=978-0-07-803841-9 |language=en}}</ref>}}). Existential quantification is distinct from [[universal quantification]] ("for all"), which asserts that the property or relation holds for ''all'' members of the domain.<ref>{{Cite web |title=Predicates and Quantifiers |url=https://www.csm.ornl.gov/~sheldon/ds/sec1.6.html |access-date=2020-09-04 |website=www.csm.ornl.gov}}</ref><ref>{{Cite web |title=1.2 Quantifiers |url=https://www.whitman.edu/mathematics/higher_math_online/section01.02.html |access-date=2020-09-04 |website=www.whitman.edu}}</ref> Some sources use the term '''existentialization''' to refer to existential quantification.<ref>{{cite book |last1=Allen |first1=Colin |url=https://books.google.com/books?id=RSTYAgAAQBAJ&pg=PA77|title=Logic Primer |last2=Hand |first2=Michael |date=2001 |publisher=MIT Press |isbn=0262303965 |language=en}}</ref>

Quantification in general is covered in the article on [[quantification (logic)]]. The existential quantifier is encoded as {{unichar|2203|THERE EXISTS}} in [[Unicode]], and as <code>\exists</code> in [[LaTeX]] and related formula editors.