Epsilon

Epsilon (uppercase Ε, lowercase ε) is the fifth letter of the Greek alphabet, corresponding phonetically to a close-mid front unrounded vowel /e/. In the system of Greek numerals it has a value of 5. It was derived from the Phoenician letter He . Letters that arose from Epsilon include the Roman E and Cyrillic Ye.

"Epsilon" ( ἒ ψιλόν, "simple e") was coined to distinguish the letter from αι, which by the medieval period was pronounced the same way.

The standard symbol for lowercase epsilon is the lunate epsilon ϵ ( $\epsilon$ in MathML), which has its origins in Medieval Greek.

In mathematical notation, the minuscule open e symbol ɛ ( $\varepsilon$ in MathML) from the extended Latin alphabet is often used interchangeably with the lunate epsilon.

The lunate epsilon ϵ is not to be confused with the set symbol ∈ or falsely recognize as the lunate version Σ.

Symbol

The upper-case Epsilon is not a commonly-used symbol outside of the Greek language because of its similarity to the Roman letter E.

The lower-case epsilon, ε/ϵ, or open e, ɛ, (see above) is used as the symbol for:

In mathematics (particularly calculus), an arbitrarily (or nearly so) small positive quantity is commonly denoted ε; see limit.
- By analogy with this, the late mathematician Paul Erdős also used the term "epsilons" to refer to children (Hoffman 1998, p. 4).
In set theory, the limit ordinal of the sequence $\omega ,\omega ^{\omega },\omega ^{\omega ^{\omega }},\dots$ .
In computing, the precision of a numeric data type.
In computer science, the empty string, though different writers use a variety of other symbols for the empty string as well, including the lower case Greek letter lambda.
In mathematics, the Levi-Civita symbol.
In mathematics, to represent the dual numbers: a + bε, with ε²=0 and ε≠0.
In physics, the permittivity of a medium.
In physics/electronics, the EMF of a circuit
In automata theory, a transition that involves no shifting of an input symbol.
In astronomy, the fifth brightest (usually) star in a constellation. See Bayer designation.
In the International Phonetic Alphabet, the open-mid front unrounded vowel, (but generally written ɛ instead of ε) as in the English word "pet" (/pɛt/)
In physics, the strain of a material (A ratio of extensions).
In astronomy, Epsilon is the name for Uranus' most distant and most visible ring.
In chemistry, the molar extinction coefficient of a chromophore.
In economics, ε refers to elasticity.

Fictional names

Epsilon in Stick Force is the name of a Steek hero.
Epsilon in Rampant Evil is the name of a stolen dragon.
Epsilon in Malaysian Pale is the name of the second solo album released by Tangerine Dream leader Edgar Froese in 1975.
Epsilon is also an Australian light-powered female-looking robot that fought Pluto in an episode of Astro Boy.
Epsilon is the primordial guide of Jess in the young adult's novel The Riddles of Epsilon by Christine Morton-Shaw.
Epsilon Eridani III is the planet that the spacestation Babylon 5 orbited in the eponymous sci-fi television series.
E-104 Epsilon is also the name of a robot in Sonic Adventure.
"Epsilon 9" is the name of the Federation space station consumed by the V'ger cloud in Star Trek: The Motion Picture.
Epsilon is the name of an unlockable creature in the game Monster Rancher 2
In Greek it is used for Epsilon Team.
"Epsilon Mirror" is the name of one of Aika's moves in the video game Skies of Arcadia.
Epsilon is the leader of the Rebellion in Mega Man X: Command Mission
"The Epsilon Program" is a mysterious cult in the video game Grand Theft Auto: San Andreas by Game Developer Rockstar North. This cult is thought to be based on Scientology. It is also a clan in SA-MP (GTA SA Multiplayer)
The Epsilon Project is a fictional experiment mentioned in the Dreamcast and Xbox versions of Dead or Alive 2 and is based around cloning.
"Epsilon" Is the beginning of some names of computer controlled clone troopers in Star Wars Battlefront for PC, Xbox and PS2.
"Epsilon" is the title of a superhero novel by John J. Rust, published through Xlibris.
Epsilon Eridani is also the name of the first planet attacked by the UNEF in The Forever War, a science fiction novel by Joe Haldeman.
"Ground Team Epsilon" was an assault team in the game "G-Police" for Playstation 1.
Epsilion is a social status for a group of all most simian people with an I.Q. of less that 50 the novel Brave New World by Aldous Huxley

Other uses

"Epsilon" is the name used by General Motors for the post-2003 Epsilon platform.
"Epsilon Events" is a company founded in 2005 by Dan Craft and James Wilmott, which has quickly developed into the leading EU dedicated conference and event provider.
"Epsilon Concepts" is the name used by a company founded in 2000 by Rob Berthume that is a premier marketing-driven web design firm in the United States.
Hurricane Epsilon, a storm of the 2005 Atlantic hurricane season.
Epsilon is the name of an open-source project, part of the Eclipse GMT project, that provides integrated languages to support various model management tasks (e.g. validation, transformation, merging, code generation etc.).

References

Hoffman, Paul; The man who loved only numbers. Hyperion, 1998. ISBN 0-7868-6362-5.