Editing Epsilon (section)

{{Short description|Fifth letter of the Greek alphabet}}
{{Distinguish|Upsilon}} <!-- Letters with similar appearance are in the "See also" section below -->
{{about|the Greek letter|other uses|Epsilon (disambiguation)|and|E (disambiguation)}}
{{use dmy dates|date=May 2024}}
{{Greek Alphabet|letter=epsilon}}
{{Orthography notation}}
'''Epsilon''' ({{IPAc-en|US|ˈ|ɛ|p|s|ᵻ|l|ɒ|n|audio=LL-Q1860 (eng)-Flame, not lame-Epilson.wav}},<ref>{{cite encyclopedia |title=epsilon |encyclopedia=Longman Pronunciation Dictionary |first=John C. |last=Wells |author-link=John C. Wells |publisher=[[Longman]] |year=1990 |page=250 |location=[[Harlow]], England |isbn=0582053838}}</ref> {{IPAc-en|UK|ɛ|p|ˈ|s|aɪ|l|ə|n}};<ref>{{cite OED|epsilon}}</ref> uppercase '''{{lang|el|Ε}}''', lowercase '''{{lang|el|ε}}''' or  '''{{lang|el|ϵ}}'''; {{langx|el|έψιλον}}) is the fifth letter of the [[Greek alphabet]], corresponding phonetically to a [[mid<!-- not close-mid, see (1999) - Illustrations of the IPA: Modern Greek. --> front unrounded vowel]] {{IPA|el|e̞|IPA}} or {{IPA|el|ɛ̝|IPA}}. In the system of [[Greek numerals]] it also has the value five. It was derived from the [[Phoenician alphabet|Phoenician letter]] [[He (letter)|He]] <span style="background-color: white;">[[File:Phoenician he.svg|20px|He]]</span>. Letters that arose from epsilon include the Roman [[E]], [[Ë]] and [[Latin epsilon|Ɛ]], and Cyrillic [[Ye (Cyrillic)|Е]], [[Ye with grave|È]], [[Yo (Cyrillic)|Ё]], [[Ukrainian Ye|Є]] and [[E (Cyrillic)|Э]]. The name of the letter was originally {{lang|grc|εἶ}} ({{IPA|grc|êː|lang|link=yes}}), but it was later changed to {{wikt-lang|grc|ἒ ψιλόν}} ({{lang|Grc-Latn|e psilon}} 'simple e') in the Middle Ages to distinguish the letter from the [[digraph (orthography)|digraph]] {{lang|grc|αι}}, a former [[diphthong]] that had come to be pronounced the same as epsilon.

The [[uppercase]] form of epsilon is identical to Latin {{angbr|E}} but has its own [[code point]] in [[Unicode]]: {{unichar|0395|Greek capital letter epsilon}}. The [[lowercase]] version has two typographical variants, both inherited from [[history of the Greek alphabet|medieval Greek handwriting]]. One, the most common in modern typography and inherited from medieval [[minuscule]], looks like a reversed number "[[3]]" and is encoded {{unichar|03B5|Greek small letter epsilon}}. The other, also known as [[#Glyph variants|lunate]] or [[uncial script|uncial]] epsilon and inherited from earlier uncial writing,<ref name="nicholas1">Nick Nicholas: [http://www.tlg.uci.edu/~opoudjis/unicode/letters.html Letters] {{Webarchive|url=https://archive.today/20121215104041/http://www.tlg.uci.edu/~opoudjis/unicode/letters.html |date=2012-12-15 }}, 2003–2008. (''Greek Unicode Issues'')</ref><ref name="colwell">{{cite book|last=Colwell|first=Ernest C.|chapter=A chronology for the letters Ε, Η, Λ, Π in the Byzantine minuscule book hand|title=Studies in methodology in textual criticism of the New Testament|year=1969|place=Leiden|publisher=Brill|pages=127}}</ref> looks like a semicircle crossed by a horizontal bar: it  is encoded {{unichar|03F5|Greek lunate epsilon symbol}}. While in normal typography these are just alternative font variants, they may have different meanings as mathematical symbols: computer systems therefore offer distinct encodings for them.<ref name="nicholas1"/> In [[TeX]], <code>\epsilon</code> ( <math>\epsilon\!</math> ) denotes the lunate form, while <code>\varepsilon</code> ( <math>\varepsilon</math> ) denotes the [[epsilon number]]. Unicode versions 2.0.0 and onwards use {{char|ɛ}} as the lowercase Greek epsilon letter,<ref>{{cite book|chapter=Code Charts|chapter-url=https://www.unicode.org/versions/Unicode2.0.0/CodeCharts1.pdf|page=130|title=The Unicode Standard, Version 2.0|ISBN=0-201-48345-9}}</ref> but in version 1.0.0, {{char|ϵ}} was used.<ref>{{cite book|chapter=Code Charts|chapter-url=https://www.unicode.org/versions/Unicode1.0.0/CodeCharts1.pdf|page=130|title=The Unicode Standard, Version 1.0|volume=1|ISBN=0-201-56788-1}}</ref> The lunate or uncial epsilon provided inspiration for the [[euro sign]], {{char|€}}.<ref name="ec.europa.eu">{{cite web|url=https://ec.europa.eu/economy_finance/euro/cash/symbol/index_en.htm |title=European Commission – Economic and Financial Affairs – How to use the euro name and symbol |publisher=Ec.europa.eu |access-date=7 April 2010 |quote= Inspiration for the € symbol itself came from the Greek epsilon, {{char|ϵ}} – a reference to the cradle of European civilization – and the first letter of the word Europe, crossed by two parallel lines to 'certify' the stability of the euro.}}</ref>

There is also a '[[Latin epsilon]]', {{angbr|ɛ}} or "open e", which looks similar to the Greek lowercase epsilon. It is encoded in Unicode as {{unichar|025B |Latin small letter open e}} and {{unichar|0190|Latin capital letter open e}} and is used as an [[International Phonetic Alphabet|IPA]] phonetic symbol. This Latin uppercase epsilon, {{char|Ɛ}}, is not to be confused with the Greek uppercase {{char|Σ}} ([[sigma]])

The lunate epsilon, {{angbr|ϵ}}, is not to be confused with the [[set membership]] symbol {{char|∈}}.  The symbol <math>\in</math>, first used in set theory and logic by [[Giuseppe Peano]] and now used in mathematics in general for set membership ("belongs to"), evolved from the letter epsilon, since the symbol was originally used as an abbreviation for the Latin word {{lang|la|'''e'''st}}.  In addition, mathematicians often read the symbol {{char|∈}} as "element of", as in "1 is an element of the natural numbers" for <math>1\in\N</math>, for example.  As late as 1960, {{char|ɛ}} itself was used for set membership, while its negation "does not belong to" (now {{char|∉}}) was denoted by {{char|ε'}} (epsilon prime).<ref>{{Cite book|title=Naive Set Theory|last=Halmos|first=Paul R.|publisher=Van Nostrand|year=1960|isbn=978-1614271314|location=New York|pages=5–6}}</ref>  Only gradually did a fully separate, stylized symbol take the place of epsilon in this role.  In a related context, Peano also introduced the use of a backwards epsilon, {{char|϶}}, for the phrase "such that", although the abbreviation ''s.t.'' is occasionally used in place of {{char|϶}} in informal cardinals.