- published: 15 Mar 2016
- views: 493
In predicate logic, universal quantification formalizes the notion that something (a logical predicate) is true for everything, or every relevant thing. The resulting statement is a universally quantified statement, and we have universally quantified over the predicate. In symbolic logic, the universal quantifier (typically Failed to parse (Missing texvc executable; please see math/README to configure.): \forall , U+2200 ∀ , a turned A) is the symbol used to denote universal quantification, and is often informally read as "given any" or "for all". Universal quantification is distinct from existential quantification ("there exists"), which asserts that the property or relation holds for at least one member of the domain.
Quantification in general is covered in the article on quantification. Symbols are encoded U+2200 ∀ for all (HTML: ∀
∀
as a mathematical symbol).
Suppose it is given that
2·0 = 0 + 0, and 2·1 = 1 + 1, and 2·2 = 2 + 2, etc.
This would seem to be a logical conjunction because of the repeated use of "and." However, the "etc." cannot be interpreted as a conjunction in formal logic. Instead, the statement must be rephrased:
Angelina Jolie ( /dʒoʊˈliː/ joh-LEE, born Angelina Jolie Voight; June 4, 1975) is an American actress and director. She has received an Academy Award, two Screen Actors Guild Awards, and three Golden Globe Awards, and was named Hollywood's highest-paid actress by Forbes in 2009 and 2011. Jolie promotes humanitarian causes, and is noted for her work with refugees as a Special Envoy and former Goodwill Ambassador for the United Nations High Commissioner for Refugees (UNHCR). She has been cited as the world's "most beautiful" woman, a title for which she has received substantial media attention.
Jolie made her screen debut as a child alongside her father Jon Voight in Lookin' to Get Out (1982), but her film career began in earnest a decade later with the low-budget production Cyborg 2 (1993). Her first leading role in a major film was in the cyber-thriller Hackers (1995). She starred in the critically acclaimed biographical television films George Wallace (1997) and Gia (1998), and won an Academy Award for Best Supporting Actress for her performance in the drama Girl, Interrupted (1999).
Mariah Carey (born March 27, 1970) is an American singer, songwriter, record producer, and actress. She made her recording debut in 1990 under the guidance of Columbia Records executive Tommy Mottola, and released her self-titled debut studio album, Mariah Carey. The album went multi-platinum and spawned four consecutive number one singles, on the U.S. Billboard Hot 100 chart. Following her marriage to Mottola in 1993, a series of hit records, including Emotions (1991), Music Box (1993) and Merry Christmas (1994), established her position as Columbia's highest-selling act. Daydream (1995), made music history when the second single, "One Sweet Day" a duet with Boyz II Men, spent a record sixteen weeks on top of the Billboard Hot 100, and remains the longest running number one song in US chart history. During the recording of the album Carey began to deviate from her pop background, and slowly traversed into R&B and Hip-hop. After her separation from Mottola, this musical change was evident with the release of Butterfly (1997).