# Existential quantification

## Mathematical use of "there exists" / From Wikipedia, the free encyclopedia

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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*)"^{[1]}). Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for *all* members of the domain.^{[2]}^{[3]} Some sources use the term **existentialization** to refer to existential quantification.^{[4]}

**Quick Facts**Type, Field ...

Type | Quantifier |
---|---|

Field | Mathematical logic |

Statement | $\exists xP(x)$ is true when $P(x)$ is true for at least one value of $x$. |

Symbolic statement | $\exists xP(x)$ |

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.