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.

Unique (DJ Encore album)

Unique is the second album by the Danish eurodance producer DJ Encore, with vocals by Swedish singer Johanna Elkesdotter, whereas the first album featured the vocals of Danish singer Engelina. It was released on May 8, 2007 on US label Koch Records.

The song "You Can Walk on Water" is a cover version of the 2002 song "Walk on Water (Baby U Can)" by Danish dance act Catch. "Out There" was originally released on DJ Encore's first album, Intuition, with vocals by Engelina.

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Unique (band)

Unique was a short-lived post-disco studio act from New York, best known for their crossover number "What I Got Is What You Need" released in 1983 for a well-established dance label, Prelude Records. The group was formed by producer/songwriter Deems J. Smith in 1982 and consists of Smith and Darryl K. Henry. The said hit song somewhat established itself on the Billboard Dance Singles and Black Singles charts and even scored over the atlantic reaching No. 27 on UK Singles Chart.

History

Around 1982, record producer Deems J. Smith hired studio musicians to appear in a project he named Unique. He was signed to dance record label Prelude and under this name released two singles: "What I Got Is What You Need" in 1983 and "You Make Me Feel So Good" in 1984. Other people involved in the group were Mona Maria Norris and Darryl K. Henry who co-wrote "What I Got Is What You Need." Smith wrote the second song alone and it was mixed by an aspiring dance-pop producer Shep Pettibone.

Chart performance

Moving

Moving or Movin' may refer to:

Moving of goods

Music

Albums

Songs

Other uses

See also

Moving (1993 film)

Moving (Japanese: お引越し, translit. Ohikkoshi) is a 1993 Japanese drama film directed by Shinji Sōmai. It was screened in the Un Certain Regard section at the 1993 Cannes Film Festival.

Cast

References

External links

Moving (Young Paperboyz album)

Moving is the debut album by the by Nigerian hip hop R&B /pop musical group Young Paperboyz, released in 2010. The album contains Young Paperboyz's first worldwide hit single, "You Know" however, the release of Moving propelled Young Paperboyz to sign a promo deal. The album performed well in stores.

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Release history

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