Epsilon

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Epsilon (uppercase Ε, lowercase ε; 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.

The name "epsilon" (ἒ ψιλόν, "simple e") was coined in the Middle Ages to distinguish the letter from the digraph αι, a former diphthong that had come to be pronounced the same as epsilon.

The uppercase form of epsilon looks essentially identical to Latin E. The lowercase version has two typographical variants, both inherited from medieval Greek handwriting. One, the most common in modern typography and inherited from medieval minuscule, looks like an inverted "3". The other, also known as lunate or uncial epsilon and inherited from earlier uncial writing,^[]^[] looks like a semicircle crossed by a horizontal bar. While in normal typography these are just alternate font variants, both may have different meanings as mathematical symbols. Computer systems therefore offer distinct encodings for both.^[] In Unicode, the character U+03F5 "Greek lunate epsilon symbol" (ϵ) is provided specifically for the lunate form. In TeX, \epsilon ( <math>\epsilon\!</math>) denotes the lunate form, while \varepsilon (<math>\varepsilon\!</math>) denotes the inverted-3 form.

There is also a Latin epsilon or "open e", which looks similar to the Greek lowercase epsilon. It is encoded in Unicode as U+025B ("Latin small letter open e", ɛ) and U+0190 ("Latin capital letter open e", Ɛ) and is used as an IPA phonetic symbol. 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).

History

Origin

The letter Ε was taken over from the Phonician letter He () when Greeks first adopted alphabetic writing. In archaic Greek writing, its shape is often still identical to the Phoenician letter. Like other Greek letters, it could face either leftwards or rightwards (), depending on the current writing direction, but just like in Phoenician, the horizontal bars always faced in the direction of writing. Archaic writing often preserves the Phoenician form with a vertical stem extending slightly below the lowest horizontal bar. In the classical era, through the influence of more cursive writing styles, the shape was simplified to the current E glyph.^[]

Sound value

The initial sound value of Ε was determined by the vowel occurring in the Phoenician letter name He, which made it a natural choice for being reinterpreted from a consonant symbol to a vowel symbol denoting an [e] sound.^[] Besides its classical Greek sound value, the short /e/ phoneme, it could initially also be used for other [e]-like sounds. For instance, in early Attic before c.500 B.C., it was used also both for the long, open /ɛː/, and for the long close /eː/. In the former role, it was later replaced in the classic Greek alphabet by Eta (Η), which was taken over from eastern Ionic alphabets, while in the latter role it was replaced by the digraph spelling ΕΙ.

Epichoric alphabets

Some dialects used yet other ways of distinguishing between various e-like sounds.

In Corinth, the normal function of Ε to denote /e/ and /ɛː/ was taken by a glyph resembling a pointed B (), while Ε was used only for long close /eː/.^[] The letter Beta, in turn, took the deviant shape .

In Sicyon, a variant glyph resembling an X () was used in the same function as Corinthian .^[]

In Thespiai (Boeotia), a special letter form consisting of a vertical stem with a single rightward-pointing horizontal bar () was used for what was probably a raised variant of /e/ in pre-vocalic environments.^[]^[] This tack glyph was used elsewhere also as a form of "Heta", i.e. for the sound /h/.

Glyph variants

After the establishment of the canonical classic Greek alphabet, new glyph variants for Ε were introduced through handwriting. In the uncial script (used for literary papyrus manuscripts in late antiquity and then in early medieval vellum codices), the "lunate" shape () became predominant. In cursive handwriting, a large number of shorthand glyphs came to be used, where the cross-bar and the curved stroke were linked in various ways.^[] Some of them resembled a modern lowercase Latin "e", some a "6" with a connecting stroke to the next letter starting from the middle, and some a combination of two small "c"-like curves. Several of these shapes were later taken over into minuscule book hand. Of the various minuscule letter shapes, the inverted-3 form became the basis for lower-case Epsilon in Greek typography during the modern era.

Uncial	Uncial variants	Cursive variants	Minuscule	Minuscule with ligatures

Uses

International Phonetic Alphabet

In the International Phonetic Alphabet, the Latin epsilon ɛ represents open-mid front unrounded vowel, as in the English word "pet" ˈpɛt.

Symbol

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

Lower case

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

Math and science

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, Hilbert introduced epsilon terms εx.φ as an extension to first order logic; see epsilon calculus.
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.
In set theory, the limit ordinal of the sequence .
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 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.

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 is a multi-platform Emacs-like programmer's text editor by Lugaru Software Ltd
Epsilon is used in the "reverse cat-face" emoticon.

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

Initial

References

1. Nick Nicholas: Letters, 2003–2008. (Greek Unicode Issues)
2. Colwell, Ernest C. (1969). "A chronology for the letters Ε, Η, Λ, Π in the Byzantine minuscule book hand". Studies in methodology in textual criticism of the New Testament. Leiden: Brill. pp. 127.
3. Jeffery, Lilian H. (1961). The local scripts of archaic Greece. Oxford: Clarendon. pp. 63–64.
4. Jeffery, Local scripts, p.24.
5. Jeffery, Local scripts, p.114.
6. Jeffery, Local scripts, p.138.
7. Jeffery, Local scripts, p.89.
8. Thompson, Edward M. (1911). An introduction to Greek and Latin palaeography. Oxford: Clarendon. pp. 191–194.

External Links

Wikipedia article on Epsilon