- published: 06 Mar 2016
- views: 2036
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:
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).
Steven Paul "Steve" Jobs (/ˈdʒɒbz/; February 24, 1955 – October 5, 2011) was an American businessman, designer and inventor. He is best known as the co-founder, chairman, and chief executive officer of Apple Inc. Through Apple, he was widely recognized as a charismatic pioneer of the personal computer revolution and for his influential career in the computer and consumer electronics fields. Jobs also co-founded and served as chief executive of Pixar Animation Studios; he became a member of the board of directors of The Walt Disney Company in 2006, when Disney acquired Pixar.
In the late 1970s, Apple co-founder Steve Wozniak engineered one of the first commercially successful lines of personal computers, the Apple II series. Jobs was among the first to see the commercial potential of Xerox PARC's mouse-driven graphical user interface, which led to the creation of the Apple Lisa and, one year later, the Macintosh. During this period he also led efforts that would begin the desktop publishing revolution, notably through the introduction of the LaserWriter and the associated PageMaker software.