In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. It is denoted by the logical operator symbol ∃ (pronounced "there exists" or "for some"), which is called the existential quantifier. Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for any members of the domain.

Symbols are encoded U+2203 ∃ there exists (HTML: ∃ ∃ as a mathematical symbol) and U+2204 ∄ there does not exist (HTML: ∄).

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

0·0 = 25, or 1·1 = 25, or 2·2 = 25, or 3·3 = 25, and so on.

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

For some natural number n, n·n = 25.

This is a single statement using existential quantification.

Donald John Trump, Sr. (born June 14, 1946) is an American business magnate, television personality and author. He is the chairman and president of The Trump Organization and the founder of Trump Entertainment Resorts. Trump's extravagant lifestyle, outspoken manner and role on the NBC reality show The Apprentice have made him a well-known celebrity who was No. 17 on the 2011 Forbes Celebrity 100 list. He is well-known as a real-estate developer who amassed vast hotel, casino, and other real-estate properties, in the New York City area and around the world.

Trump is the son of Fred Trump, a wealthy New York City real-estate developer. He worked for his father's firm, Elizabeth Trump & Son, while attending the Wharton School of the University of Pennsylvania, and in 1968 officially joined the company. He was given control of the company in 1971 and renamed it The Trump Organization.

In 2010, Trump expressed an interest in becoming a candidate for President of the United States in the 2012 election. In May 2011, he announced he would not be a candidate, but a few weeks later he said he had not completely ruled out the possibility. In December 2011, Trump was suggested as a possible Vice Presidential selection by Michele Bachmann. Bachmann has since suspended her presidential campaign.