- published: 16 Jun 2009
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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.
Stephen William Hawking, CH, CBE, FRS, FRSA (born 8 January 1942) is a British theoretical physicist, cosmologist, and author. His key scientific works to date have included providing, with Roger Penrose, theorems regarding gravitational singularities in the framework of general relativity, and the theoretical prediction that black holes should emit radiation, which is today known as Hawking radiation (or sometimes as Bekenstein–Hawking radiation).
He is an Honorary Fellow of the Royal Society of Arts, a lifetime member of the Pontifical Academy of Sciences, and in 2009 was awarded the Presidential Medal of Freedom, the highest civilian award in the United States. Hawking was the Lucasian Professor of Mathematics at the University of Cambridge between 1979 and 2009. Subsequently, he became research director at the university's Centre for Theoretical Cosmology.
Hawking has a motor neurone disease related to amyotrophic lateral sclerosis, a condition that has progressed over the years. He is now almost completely paralysed and communicates through a speech generating device. He has been married twice and has three children. Hawking has achieved success with works of popular science in which he discusses his own theories and cosmology in general; these include A Brief History of Time, which stayed on the British Sunday Times best-sellers list for a record-breaking 237 weeks.