Epsilon

Greek alphabet

Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega
History
Archaic local variants · · · · ·
Ligatures (ϛ, ȣ, ϗ) · Diacritics
Numerals: (6) · (90) · (900)
In other languages
Bactrian · Coptic · Albanian
Scientific symbols
Book · Category · Commons

Epsilon (uppercase Ε, lowercase ε or lunate 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.

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,^[1]^[2] looks like a semicircle crossed by a horizontal bar. While in normal typography these are just alternate font variants, they may have different meanings as mathematical symbols. Computer systems therefore offer distinct encodings for them.^[1] In Unicode, the character U+03F5 "Greek lunate epsilon symbol" (ϵ) is provided specifically for the lunate form. In TeX, \epsilon ( $\epsilon\!$ ) denotes the lunate form, while \varepsilon ( $\varepsilon\!$ ) 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).

1 History
2 Uses
- 2.1 International Phonetic Alphabet
- 2.2 Symbol
3 Unicode
4 Initial
5 References
6 Further reading

History

Origin

The letter Ε was taken over from the Phoenician 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.^[3]

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.^[4] 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/.^[5] 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 .^[6]

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.^[1]^[7] 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.^[8] 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.

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, Hilbert introduced epsilon terms $\epsilon x.\phi$ 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 $\omega,\omega^\omega,\omega^{\omega^\omega},\dots$ .
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 upper-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.

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

^ ^a ^b ^c Nick Nicholas: Letters, 2003–2008. (Greek Unicode Issues)
^ 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.
^ Jeffery, Lilian H. (1961). The local scripts of archaic Greece. Oxford: Clarendon. pp. 63–64.
^ Jeffery, Local scripts, p.24.
^ Jeffery, Local scripts, p.114.
^ Jeffery, Local scripts, p.138.
^ Jeffery, Local scripts, p.89.
^ Thompson, Edward M. (1911). An introduction to Greek and Latin palaeography. Oxford: Clarendon. pp. 191–194.