Uniqueness quantification

In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists. In mathematical logic, this sort of quantification is known as uniqueness quantification or unique existential quantification.

Uniqueness quantification is often denoted with the symbols "∃!" or ∃₌₁". For example, the formal statement

may be read aloud as "there is exactly one natural number n such that n - 2 = 4".

Proving uniqueness

The most common technique to proving uniqueness is to first prove existence of entity with the desired condition; then, to assume there exist two entities (say, a and b) that should both satisfy the condition, and logically deduce their equality, i.e. a = b.

As a simple high school example, to show x + 2 = 5 has only one solution, we assume there are two solutions first, namely, a and b, satisfying x + 2 = 5. Thus

By transitivity of equality,

By cancellation,

This simple example shows how a proof of uniqueness is done, the end result being the equality of the two quantities that satisfy the condition. However, that existence/expressibility must be proven before uniqueness, or else we cannot even assume the existence of those two quantities to begin with our current knowledge to date.

Video game

A video game is an electronic game that involves human interaction with a user interface to generate visual feedback on a video device such as a TV screen or computer monitor. The word video in video game traditionally referred to a raster display device, but it now implies any type of display device that can produce two- or three-dimensional images. Video games are sometimes believed to be a form of art, but this designation is controversial.

The electronic systems used to play video games are known as platforms; examples of these are personal computers and video game consoles. These platforms range from large mainframe computers to small handheld computing devices. Specialized video games such as arcade games, while common in the 1980s, have gradually declined in use due to the widespread availability of home video game devices (e.g., PlayStation 4 and Xbox One) and video games on desktop and laptop computers and smartphones.

The input device used for games, the game controller, varies across platforms. Common controllers include gamepads, mouses, keyboards, joysticks, the touchscreens of mobile devices and buttons. In addition to video and (in most cases) audio feedback, some games include haptic, vibration or force feedback peripherals.

Popular culture

Popular culture or pop culture is the entirety of ideas, perspectives, attitudes, images, and other phenomena that are within the mainstream of a given culture, especially Western culture of the early to mid 20th century and the emerging global mainstream of the late 20th and early 21st century. Heavily influenced by mass media, this collection of ideas permeates the everyday lives of the society. The most common pop culture categories are: entertainment (movies, music, TV), sports, news (as in people/places in news), politics, fashion/clothes, technology, and slang.

Popular culture is often viewed as being trivial and "dumbed down" in order to find consensual acceptance throughout the mainstream. As a result, it comes under heavy criticism from various non-mainstream sources (most notably religious groups and countercultural groups) which deem it superficial, consumerist, sensationalist, or corrupt.

History and definitions

The term "popular culture" was coined in the 19th century or earlier. Traditionally, popular culture was associated with poor education and the lower classes, as opposed to the "official culture" and higher education of the upper classes.

Real World

The real world is another term for reality.

Real World may also refer to:

Television

Music

Jon Savage

Jon Savage (born Jonathan Malcolm Sage; 2 September 1953 in Paddington, London) is an English writer, broadcaster and music journalist, best known for his award winning history of the Sex Pistols and punk music, England's Dreaming, published in 1991.

Career

Savage was a high-profile writer during the glory days of British punk and wrote articles on all the major punk acts. He wrote and published a fanzine called London's Outrage in 1976, and in 1977 began working as a journalist for Sounds, which was, at that time, one of the UK's three major music papers, along with the New Musical Express and Melody Maker. Savage interviewed punk, new wave and electronic music artists for Sounds. At that time, he also wrote for the West Coast fanzines Search and Destroy, Bomp! and Slash.

In 1979 he moved to Melody Maker, and a year later to the newly founded pop culture magazine The Face. Throughout the decade, Savage wrote for The Observer and the New Statesman, providing high-brow commentary on popular culture.