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

Daniel Küblböck

Daniel Küblböck (born 27 August 1985 in Hutthurm, Lower Bavaria) is a German pop-singer and actor who achieved short-lived celebrity in 2003, in the media-circus that surrounded the first season of Deutschland sucht den Superstar (DSDS), the German version of Pop Idol, in which he came third. He was briefly promoted as Daniel K, but reverted to his legal name when it emerged that this name had already been trademarked.

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Daniel Inouye

Daniel Ken "Dan" Inouye (Japanese: 井上 建, Hepburn: Inoue Ken, pronounced /iːˈnoʊwɛ/ ē-NOH-weh; September 7, 1924 – December 17, 2012) was a United States Senator from Hawaii from 1963 to 2012. He was a member of the Democratic Party, and he was President pro tempore of the United States Senate from 2010 until his death in 2012, making him the highest-ranking Asian American politician in U.S. history. Inouye also served as chairman of the U.S. Senate Committee on Appropriations.

Inouye fought in World War II as part of the 442nd Infantry Regiment. He lost his right arm to a grenade wound and received several military decorations. Returning to Hawaii, he earned a law degree and was elected to Hawaii's territorial House of Representatives in 1953, and to the territorial Senate in 1957. When Hawaii achieved statehood in 1959, Inouye was elected as its first member of the U.S. House of Representatives, and in 1962 he was first elected to the U.S. Senate. Inouye was the most senior U.S. senator at the time of his death. He is one of the longest-serving U.S. Senators in history, second only to Robert Byrd. Inouye was the first Japanese American to serve in the U.S. House of Representatives and later the first in the U.S. Senate. He never lost an election in 58 years as an elected official, and exercised an outsize influence on Hawaii politics. At the time of his death, Inouye was the second-oldest sitting U.S. senator, after Frank Lautenberg of New Jersey, who also died soon afterwards.