Epsilon

Epsilon (uppercase Ε, lowercase ε; Greek: Έψιλον) 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 in the Middle Ages to distinguish the letter from the diphthong αι, which started being pronounced the same way during the period of New Testament Greek.

There is also a Latin epsilon – or "open e" – ɛ (\varepsilon, $\varepsilon$ , in LaTeX), which looks similar to the Greek lowercase epsilon. Another variant is the lunate epsilon symbol ϵ (\epsilon, $\epsilon \,$ , in LaTeX), which has its origins in medieval Greek uncial script but is mostly used in mathematics today.^[1] The lunate or uncial epsilon has also provided inspiration for the euro sign (€).

The lunate epsilon (ϵ) is not to be confused with the set membership symbol (∈), nor should the Latin uppercase epsilon (Ɛ) be confused with the Greek uppercase sigma (Σ).

Symbol

The uppercase Epsilon is not commonly used outside of the Greek language because of its similarity to the Latin letter E.

The Greek lowercase epsilon ε, the lunate epsilon symbol ϵ, or the Latin lowercase epsilon ɛ (see above) is used as the symbol for:

In mathematics (particularly calculus), an arbitrarily small positive quantity is commonly denoted ε; see (ε, δ)-definition of limit.
- By analogy with this, the late mathematician Paul Erdős also used the term "epsilons" to refer to children (Hoffman 1998, p. 4).
In mathematics, the Levi-Civita symbol.
In mathematics, to represent the dual numbers: a + bε, with ε²=0 and ε≠0.
In mathematics, sometimes used to denote the Heaviside step function.^{[citation needed]}
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 and floating-point machine epsilon.
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 physics, the permittivity of a medium.
In physics and electronics, the emf of a circuit
In physics, the strain of a material (a ratio of extensions).
In automata theory, a transition that involves no shifting of an input symbol.
In astronomy, the fifth-brightest star in a constellation (see Bayer designation).
In linguistics and the International Phonetic Alphabet, the Latin epsilon ɛ represents open-mid front unrounded vowel, as in the English word "pet" (/pɛt/).
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.
In statistics, to refer to error terms.
In agriculture, to represent the "photosynthetic efficiency" of a particular plant or crop.

Fictional names

In the popular web series "Red vs. Blue", Epsilon is the name of Agent Washington's AI, possessing memories from the breaking of the Alpha AI by Project Freelancer.
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 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 is an otherworldy being in the book The Riddles of Epsilon by Christine Morton-Shaw.
"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.
The Epsilon Project is a fictional experiment mentioned in the Dreamcast and Xbox versions of Dead or Alive 2 and is based on cloning.
Epsilon is the lowest of five social castes in the Aldous Huxley novel Brave New World.
"Plan Epsilon" was one of many plans to restore Doctor Doom to life in the event of his death, as shown in Fantastic Four issue no. 246, written by Stan Lee.
Epsilon-Eagle is the name of the protagonist in the Sega Mega Drive game Alien Soldier.
Epsilon was the name given to one of the ground support teams in the Sony Playstation game G-Police.
Epsilon is the name of the newly resurrected Yuri Faction in the Yuri's Revenge mod Mental Omega.
Epsilon was one of the warriors of Asgard in the Anime series Saint Seiya, Fenrir Epsilon, The Northern Wolf, when Dragon Shiryu had to fight for his life against him on his way to rescue Hilda.
Epsilon was the name of the chef dog in the Pixar movie Up when Carl and Russell are in Muntz's lair.
"Epsilon Knight" is the name of a racer in the Extreme-G racing game series who, if controlled by the computer, always happened to finish 5th.
Epsilon was a man-made God in the game AdventureQuest.
Epsilon was an alternative title to the Australian movie Alien Visitor.
Epsilon is a character in Megaman Zero 2 where you fight him as the final boss.

Other uses

"Epsilon" is the name used by General Motors for the post-2003 Epsilon platform.
Epsilon Euskadi, a carmaker and EpsilonEuskadi LMP1 car.
Barazi-Epsilon, a manufacturer in the 2009 Superleague Formula season for the Olympique Lyonnais car.
Hurricane Epsilon, a storm of the 2005 Atlantic hurricane season.
Epsilon TB-30 is a training aircraft made by Socata and used by the French, Portuguese, Senegalese and Togo airforces. Introduced in 1984 it provides basic and intermediate training, and has a 300 hp lycoming engine.
Stars Epsilon Eridani and 40 Epsilon.

Epsilon and its derivatives in Unicode

Unicode	Sample	Description	Notes on usage
U+0395	Ε	Greek capital letter epsilon	Greek alphabet: close-mid front unrounded vowel /e/; uppercase for U+03B5
U+03B5	ε	Greek small letter epsilon	lowercase for U+0395
U+03F5	ϵ	Greek lunate epsilon symbol	mathematics
U+03F6	϶	Greek reversed lunate epsilon symbol	mathematics
U+0045	E	Latin capital letter e	Latin alphabet; uppercase for U+0065
U+0065	e	Latin small letter e	IPA: close-mid front unrounded vowel; lowercase for U+0045
U+018E	Ǝ	Latin capital letter reversed e	Pan-Nigerian alphabet; African reference alphabet; uppercase for U+01DD
U+018F	Ə	Latin capital letter schwa	Latin Azerbaijani and Chechen alphabets: near-open front unrounded vowel /æ/; Uniform Turkic Alphabet; uppercase for U+0259
U+0190	Ɛ	Latin capital letter open e	Niger-Congo languages; African reference alphabet; uppercase for U+025B
U+01DD	ǝ	Latin small letter turned e	lowercase for U+018E
U+0258	ɘ	Latin small letter reversed e	IPA: close-mid central unrounded vowel
U+0259	ə	Latin small letter schwa	IPA: mid central vowel; lowercase for U+018F
U+025B	ɛ	Latin small letter open e	IPA: open-mid front unrounded vowel; lowercase for U+0190
U+025C	ɜ	Latin small letter reversed open e	IPA: open-mid central unrounded vowel
U+0404	Є	Cyrillic capital letter Ukrainian ye	Ukrainian and Rusyn languages: /je/, or the iotated vowel sound /e/ after a palatalized consonant; uppercase for U+0454
U+0415	Е	Cyrillic capital letter ye	Belarusian and Russian languages: a palatalizing vowel; Bulgarian, Macedonian, Serbian, and Ukrainian languages: close-mid front unrounded vowel /e/ or open-mid front unrounded vowel /ɛ/; uppercase for U+0435
U+042D	Э	Cyrillic capital letter e	Belarusian and Russian languages: close-mid front unrounded vowel /e/ or open-mid front unrounded vowel /ɛ/; uppercase for U+044D
U+0435	е	Cyrillic small letter ye	lowercase for U+0415
U+044D	э	Cyrillic small letter e	lowercase for U+042D
U+0454	є	Cyrillic small letter Ukrainian ye	lowercase for U+0404
U+04D8	Ә	Cyrillic capital letter schwa	Bashkir, Kalmyk, Kazakh and Tatar (and formerly Azeri) languages: near-open front unrounded vowel /æ/; Dungan language: close-mid back unrounded vowel /ɤ/; Kurdish language: mid central vowel /ə/; Abkhaz language: labialization of the preceding consonant /ʷ/; uppercase for U+04D9
U+04D9	ә	Cyrillic small letter schwa	lowercase for U+04D8
U+20AC	€	euro sign	currency designator
U+212E	℮	estimated sign	prepackaged goods within the EU
U+2203	∃	there exists	mathematics
U+2208	∈	element of	mathematics
U+2209	∉	not an element of	mathematics
U+220A	∊	small element of	mathematics
U+220B	∋	contains as member	mathematics
U+220C	∌	does not contain as member	mathematics
U+220D	∍	small contains as member	mathematics

References

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

^ Nick Nicholas: Letters, 2003–2008. (Greek Unicode Issues)

[1] Nick Nicholas: Letters, 2003–2008. (Greek Unicode Issues)

[1]