Epsilon

<h2 id="history">History</h2>
<h3>Origin</h3>
<p>The letter ⟨Ε⟩ was adopted from the <a href="/facts/Phoenician_alphabet/Vr4smuYg">Phoenician</a> letter <a href="/facts/He_(letter)/xX9tL4gb">He</a> () when Greeks first adopted alphabetic writing. In archaic Greek writing, its shape is often still identical to that of the Phoenician letter. Like other Greek letters, it could face either leftward or rightward (), depending on the current writing direction, but, just as 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.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a>
</p>
<h3>Sound value</h3>
<p>While the original pronunciation of the Phoenician letter <i>He</i> was [h], the earliest Greek sound value of Ε was determined by the vowel occurring in the Phoenician letter name, which made it a natural choice for being reinterpreted from a consonant symbol to a vowel symbol denoting an [e] sound.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> 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 <a href="/facts/Attic_Greek/C6Ix7vNu">Attic</a> before c. 500 BC, it was used also both for the long, <a href="/facts/Open-mid_vowel/qkco8QqT">open</a> /ɛː/, and for the long <a href="/facts/Close-mid_vowel/rK07wQEd">close</a> /eː/. In the former role, it was later replaced in the classic Greek alphabet by <a href="/facts/Eta/jnxIHnSd">Eta</a> (⟨Η⟩), which was taken over from eastern <a href="/facts/Ionic_Greek/5yRPYbuo">Ionic</a> alphabets, while in the latter role it was replaced by the <a href="/facts/Digraph_(orthography)/wp3UgEyU">digraph</a> ⟨ΕΙ⟩.
</p>
<h3><a href="/facts/Archaic_Greek_alphabets/hkBDo1WD">Epichoric</a> alphabets</h3>
<p>Some dialects used yet other ways of distinguishing between various e-like sounds.
</p><p>In <a href="/facts/Ancient_Corinth/8g6C4eQ0">Corinth</a>, 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/.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> The letter <a href="/facts/Beta/a8rauGSd">Beta</a>, in turn, took the deviant shape .
</p><p>In <a href="/facts/Sicyon/1nq6hQAE">Sicyon</a>, a variant glyph resembling an ⟨X⟩ () was used in the same function as Corinthian .<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a>
</p><p>In <a href="/facts/Thespiae/gEmzTK5T">Thespiai</a> (<a href="/facts/Boeotia/V8Prmucy">Boeotia</a>), a special letter form consisting of a vertical stem with a single rightward-pointing horizontal bar () was used for what was probably a <a href="/facts/Close_vowel/Ne6tHQHR">raised</a> variant of /e/ in pre-vocalic environments.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a><a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> This tack glyph was used elsewhere also as a form of "<a href="/facts/Heta/B9KPqfhW">Heta</a>", i.e. for the sound /h/.
</p>
<h3>Glyph variants</h3>
<p>After the establishment of the canonical Ionian (Euclidean) <a href="/facts/Greek_alphabet/1cHwB8Dg">Greek alphabet</a>, new glyph variants for Ε were introduced through handwriting. In the <a href="/facts/Uncial_script/uz6CgI4u">uncial script</a> (used for literary <a href="/facts/Papyrus/RMbJNcXu">papyrus</a> manuscripts in late antiquity and then in early medieval <a href="/facts/Vellum/YVaKAeCU">vellum</a> codices), the "<a href="/facts/Lunate/NrIbxKJU">lunate</a>" shape () became predominant. In <a href="/facts/Cursive/sbW2bKYq">cursive</a> handwriting, a large number of shorthand glyphs came to be used, where the cross-bar and the curved stroke were linked in various ways.<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> 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 <a href="/facts/Minuscule_Greek/14EXbKcl">minuscule</a> 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.
</p>
<table><tbody><tr><th>Uncial</th><th>Uncial variants</th><th>Cursive variants</th><th>Minuscule</th><th>Minuscule with ligatures</th></tr><tr><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
<h2 id="uses">Uses</h2>
<h3>International Phonetic Alphabet</h3>
<p>Despite its pronunciation as <a href="/facts/Mid_front_unrounded_vowel/wJxU5vKm">mid</a>, in the <a href="/facts/International_Phonetic_Alphabet/2e7jmUaG">International Phonetic Alphabet</a>, the Latin epsilon /ɛ/ represents <a href="/facts/Open-mid_front_unrounded_vowel/aDRvwE46">open-mid front unrounded vowel</a>, as in the English word <i>pet</i> /pɛt/.
</p>
<h3>Symbol</h3>
<p>The uppercase Epsilon is not commonly used outside of the Greek language because of its similarity to the <a href="/facts/Latin_alphabet/pqWVHpBz">Latin</a> letter <a href="/facts/E/0G2cAFzu">E</a>. However, it is commonly used in <a href="/facts/Structural_mechanics/RbhbXjNT">structural mechanics</a> with <a href="/facts/Young%2527s_Modulus/MV5JMCIM">Young's Modulus</a> equations for calculating tensile, compressive and areal <a href="/facts/Deformation_(mechanics)/xK7R59oI">strain</a>.
</p><p>The Greek lowercase epsilon ε, the lunate epsilon symbol ϵ, and the <a href="/facts/Latin_epsilon/9lLWc8Bb">Latin lowercase epsilon</a> ɛ (see above) are used in a variety of places:
</p>
<ul><li>In <a href="/facts/Engineering_mechanics/rUlbDdob">engineering mechanics</a>, strain calculations ϵ = increase of length / original length. Usually this relates to extensometer testing of metallic materials.</li>
<li>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>
<ul><li>(In early <a href="/facts/Calculus/MEmUTYoz">calculus</a> or <a href="/facts/Nonstandard_analysis/lEpNpWMB">nonstandard analysis</a>) An infinitesimally small positive quantity is commonly denoted ε.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a>
<ul><li>(In <a href="/facts/Mathematical_analysis/XXeR26Ih">analysis</a>) By extension, a quantity thought of as "small", "negligible", or, especially, "arbitrarily small", is often denoted ε. For instance, quantities subject to a <a href="/facts/Limit_(mathematics)/j8JBhj4e">limit</a> which takes them towards zero are often denoted ε; see <a href="/facts/(%25CE%25B5%2c_%25CE%25B4)-definition_of_limit/3Yd7BdvM">(ε, δ)-definition of limit</a>.<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a></li></ul></li>
<li><a href="/facts/David_Hilbert/1vhlHn4b">Hilbert</a> introduced epsilon terms 
  
    
      
        ϵ
        x
        .
        ϕ
      
    
    {\displaystyle \epsilon x.\phi }
  
 as an extension to <a href="/facts/First-order_logic/lcISqWIg">first-order logic</a>; see <a href="/facts/Epsilon_calculus/yx7TDJjE">epsilon calculus</a>.</li>
<li>it is used to represent the <a href="/facts/Levi-Civita_symbol/WBKUA3Tw">Levi-Civita symbol</a>.</li>
<li>it is used to represent <a href="/facts/Dual_number/DntuRu3F">dual numbers</a>: 
  
    
      
        a
        +
        b
        ε
      
    
    {\displaystyle a+b\varepsilon }
  
, with 
  
    
      
        
          ε
          
            2
          
        
        =
        0
      
    
    {\displaystyle \varepsilon ^{2}=0}
  
 and 
  
    
      
        ε
        ≠
        0
      
    
    {\displaystyle \varepsilon \neq 0}
  
.<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a></li>
<li>it is sometimes used to denote the <a href="/facts/Heaviside_step_function/bgsUtxgP">Heaviside step function</a>.<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a></li>
<li>in <a href="/facts/Set_theory/1ptfsvUP">set theory</a>, the <a href="/facts/Epsilon_numbers_(mathematics)/t7w8KgA9">epsilon numbers</a> are <a href="/facts/Ordinal_number/GelFLjJt">ordinal numbers</a> that satisfy the <a href="/facts/Fixed_point_(mathematics)/vVVddTKc">fixed point</a> ε = ωε. The first epsilon number, ε0, is the <a href="/facts/Limit_ordinal/jPCCoPuP">limit ordinal</a> of the set {ω, ωω, ωωω, ...}.</li>
<li>in numerical analysis and statistics it is used as the <a href="/facts/Error_term/yA9Yc2mT">error term</a></li>
<li>in <a href="/facts/Group_theory/NfowcI5H">group theory</a> it is used as the <a href="/facts/Idempotent/khbSpexv">idempotent</a> group when e is in use as a variable name</li></ul></li>
<li>In <a href="/facts/Computer_science/lN3pEyPz">computer science</a>
<ul><li>it often represents the <a href="/facts/Empty_string/T7udJlmQ">empty string</a>, though different writers use a variety of other symbols for the empty string as well; usually the lower-case Greek letter <a href="/facts/Lambda/ykr3WSse">lambda</a> (λ).</li>
<li>the <a href="/facts/Machine_epsilon/Ujsx0nA5">machine epsilon</a> indicates the upper bound on the relative error due to rounding in floating point arithmetic.<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a></li></ul></li>
<li>In <a href="/facts/Physics/a7aH2y08">physics</a>,
<ul><li>it indicates the <a href="/facts/Permittivity/Sd3WtgT1">permittivity</a> of a medium; with the subscript 0 (ε0) it is the <a href="/facts/Permittivity_of_free_space/gWRUhPGY">permittivity of free space</a>.<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a></li>
<li>it can also indicate the <a href="/facts/Strain_(materials_science)/xK7R59oI">strain</a> of a material (a ratio of extensions).<a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a></li>
<li>in <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, it usually indicates the <a href="/facts/Dimensional_regularization/w6T8q6u7">dimensional regularization</a> parameter.<a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a></li></ul></li>
<li>In <a href="/facts/Automata_theory/Q6BmPv63">automata theory</a>, it shows a transition that involves no shifting of an input symbol.</li>
<li>In <a href="/facts/Astronomy/0ArJVM1p">astronomy</a>,
<ul><li>it stands for the fifth-brightest star in a <a href="/facts/Constellation/nBQqgW8A">constellation</a> (see <a href="/facts/Bayer_designation/KU2DVT47">Bayer designation</a>).</li>
<li>Epsilon is the name for the most distant and most visible ring of <a href="/facts/Uranus/x7YwT1ar">Uranus</a>.</li>
<li>In <a href="/facts/Planetary_science/ocX6rp0d">planetary science</a>, ε denotes the <a href="/facts/Axial_tilt/kt7KwL3v">axial tilt</a>.<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a></li></ul></li>
<li>In <a href="/facts/Chemistry/SrNqkGVm">chemistry</a>, it represents the <a href="/facts/Molar_extinction_coefficient/TwglQEAW">molar extinction coefficient</a> of a <a href="/facts/Chromophore/9RykVkek">chromophore</a>.</li>
<li>In <a href="/facts/Economics/HYctA2Dn">economics</a>, ε refers to <a href="/facts/Elasticity_(economics)/p4Kj7kdQ">elasticity</a>.<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a></li>
<li>In <a href="/facts/Statistics/DNPsKGYU">statistics</a>,
<ul><li>it is used to refer to <a href="/facts/Errors_and_residuals_in_statistics/Ef0LgAS4">error terms</a>.</li>
<li>it also can to refer to the degree of <a href="/facts/Mauchly%2527s_sphericity_test/16X4ncaM">sphericity</a> in <a href="/facts/Repeated_measures_design/gQ7qjgvY">repeated measures ANOVAs</a>.</li></ul></li>
<li>In <a href="/facts/Agronomy/8pvE8bmm">agronomy</a>, it is used to represent the "<a href="/facts/Photosynthetic/TMV7w693">photosynthetic</a> efficiency" of a particular plant or crop.</li></ul>
<h2 id="unicode">Unicode</h2>
<p>For accented Greek characters, see <a href="/facts/Greek_diacritics/qwHge41z">Greek diacritics: Computer encoding</a>.
</p>
<ul><li>U+0190 Ɛ <a href="/facts/%25C6%2590/0G2cAFzu">LATIN CAPITAL LETTER OPEN E</a></li>
<li>U+025B ɛ LATIN SMALL LETTER OPEN E</li>
<li>U+025C ɜ LATIN SMALL LETTER REVERSED OPEN E</li>
<li>U+025D ɝ LATIN SMALL LETTER REVERSED OPEN E WITH HOOK</li>
<li>U+025E ɞ LATIN SMALL LETTER CLOSED REVERSED OPEN E</li>
<li>U+029A ʚ LATIN SMALL LETTER CLOSED OPEN E</li>
<li>U+0388 Έ GREEK CAPITAL LETTER EPSILON WITH TONOS</li>
<li>U+0395 Ε GREEK CAPITAL LETTER EPSILON (&Epsilon;)</li>
<li>U+03AD έ GREEK SMALL LETTER EPSILON WITH TONOS</li>
<li>U+03B5 ε GREEK SMALL LETTER EPSILON (&epsi;, &epsilon;) (\varepsilon in TeX)</li>
<li>U+03F5 ϵ GREEK LUNATE EPSILON SYMBOL (&epsiv;, &straightepsilon;, &varepsilon;) (\epsilon in TeX)</li>
<li>U+03F6 ϶ GREEK REVERSED LUNATE EPSILON SYMBOL (&backepsilon;, &bepsi;)</li>
<li>U+1D08 ᴈ LATIN SMALL LETTER TURNED OPEN E</li>
<li>U+1D4B ᵋ MODIFIER LETTER SMALL OPEN E</li>
<li>U+1D4C ᵌ MODIFIER LETTER SMALL TURNED OPEN E</li>
<li>U+1D93 ᶓ LATIN SMALL LETTER OPEN E WITH RETROFLEX HOOK</li>
<li>U+1D94 ᶔ LATIN SMALL LETTER REVERSED OPEN E WITH RETROFLEX HOOK</li>
<li>U+1D9F ᶟ MODIFIER LETTER SMALL REVERSED OPEN E</li>
<li>U+2377 ⍷ APL FUNCTIONAL SYMBOL EPSILON UNDERBAR</li>
<li>U+2C88 Ⲉ COPTIC CAPITAL LETTER EIE</li>
<li>U+2C89 ⲉ COPTIC SMALL LETTER EIE</li>
<li>U+2CB6 Ⲷ COPTIC CAPITAL LETTER CRYPTOGRAMMIC EIE</li>
<li>U+2CB7 ⲷ COPTIC SMALL LETTER CRYPTOGRAMMIC EIE</li>
<li>U+A7AB Ɜ LATIN CAPITAL LETTER REVERSED OPEN E</li>
<li>U+1078F 𐞏 MODIFIER LETTER SMALL CLOSED REVERSED OPEN E</li>
<li>U+1D6AC 𝚬 MATHEMATICAL BOLD CAPITAL EPSILON<a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a></li>
<li>U+1D6C6 𝛆 MATHEMATICAL BOLD SMALL EPSILON</li>
<li>U+1D6DC 𝛜 MATHEMATICAL BOLD EPSILON SYMBOL</li>
<li>U+1D6E6 𝛦 MATHEMATICAL ITALIC CAPITAL EPSILON</li>
<li>U+1D700 𝜀 MATHEMATICAL ITALIC SMALL EPSILON</li>
<li>U+1D716 𝜖 MATHEMATICAL ITALIC EPSILON SYMBOL</li>
<li>U+1D720 𝜠 MATHEMATICAL BOLD ITALIC CAPITAL EPSILON</li>
<li>U+1D73A 𝜺 MATHEMATICAL BOLD ITALIC SMALL EPSILON</li>
<li>U+1D750 𝝐 MATHEMATICAL BOLD ITALIC EPSILON SYMBOL</li>
<li>U+1D75A 𝝚 MATHEMATICAL SANS-SERIF BOLD CAPITAL EPSILON</li>
<li>U+1D774 𝝴 MATHEMATICAL SANS-SERIF BOLD SMALL EPSILON</li>
<li>U+1D78A 𝞊 MATHEMATICAL SANS-SERIF BOLD EPSILON SYMBOL</li>
<li>U+1D794 𝞔 MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL EPSILON</li>
<li>U+1D7AE 𝞮 MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL EPSILON</li>
<li>U+1D7C4 𝟄 MATHEMATICAL SANS-SERIF BOLD ITALIC EPSILON SYMBOL</li></ul>

<h2 id="initial">Initial</h2>

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/%25D0%2595/1BWzBAPx">Е</a> and <a href="/facts/%25D0%2595/1BWzBAPx">е</a>, the letter Ye  of the Cyrillic alphabet</li>
<li>Є є, <a href="/facts/Ukrainian_Ye/JQYyGA6u">Ukrainian Ye</a></li>
<li>Ԑ ԑ, <a href="/facts/Reversed_Ze/3bu6SB0U">Reversed Ze</a></li>
<li><a href="/facts/E_(disambiguation)/Rk0NTasp">E (disambiguation)</a></li></ul>

<h2 id="further-reading">Further reading</h2>

Look up <i>Ε</i> or <i>ɛ</i> in Wiktionary, the free dictionary.

<ul><li><a href="/facts/Paul_Hoffman_(science_writer)/vphVpxK8">Hoffman, Paul</a> (1998). <i><a href="/facts/The_Man_Who_Loved_Only_Numbers/CBVdwjTm">The Man Who Loved Only Numbers</a></i>. Hyperion. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-7868-6362-5.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Wells, John C. (1990). "epsilon". Longman Pronunciation Dictionary. Harlow, England: Longman. p. 250. ISBN 0582053838. <a href="0582053838" target="_blank">0582053838</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>"epsilon". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.) <a href="https://www.oed.com/search/dictionary/?q=epsilon" target="_blank">https://www.oed.com/search/dictionary/?q=epsilon</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Nick Nicholas: Letters Archived 2012-12-15 at archive.today, 2003–2008. (Greek Unicode Issues) <a href="http://www.tlg.uci.edu/~opoudjis/unicode/letters.html" target="_blank">http://www.tlg.uci.edu/~opoudjis/unicode/letters.html</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>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. p. 127. <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Nick Nicholas: Letters Archived 2012-12-15 at archive.today, 2003–2008. (Greek Unicode Issues) <a href="http://www.tlg.uci.edu/~opoudjis/unicode/letters.html" target="_blank">http://www.tlg.uci.edu/~opoudjis/unicode/letters.html</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>"Code Charts" (PDF). The Unicode Standard, Version 2.0. p. 130. ISBN 0-201-48345-9. <a href="0-201-48345-9" target="_blank">0-201-48345-9</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>"Code Charts" (PDF). The Unicode Standard, Version 1.0. Vol. 1. p. 130. ISBN 0-201-56788-1. <a href="0-201-56788-1" target="_blank">0-201-56788-1</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>"European Commission – Economic and Financial Affairs – How to use the euro name and symbol". Ec.europa.eu. Retrieved 7 April 2010. Inspiration for the € symbol itself came from the Greek epsilon, 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. <a href="https://ec.europa.eu/economy_finance/euro/cash/symbol/index_en.htm" target="_blank">https://ec.europa.eu/economy_finance/euro/cash/symbol/index_en.htm</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
<li id="fn:9"><p>Halmos, Paul R. (1960). Naive Set Theory. New York: Van Nostrand. pp. 5–6. ISBN 978-1614271314. {{cite book}}: ISBN / Date incompatibility (help) <a href="978-1614271314" target="_blank">978-1614271314</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li>
<li id="fn:10"><p>Jeffery, Lilian H. (1961). The Local Scripts of Archaic Greece. Oxford: Clarendon. pp. 63–64. <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li>
<li id="fn:11"><p>Jeffery, Local Scripts of Archaic Greece, p. 24. <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li>
<li id="fn:12"><p>Jeffery, Local Scripts of Archaic Greece, p. 114. <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li>
<li id="fn:13"><p>Jeffery, Local Scripts of Archaic Greece, p. 138. <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li>
<li id="fn:14"><p>Nicholas, Nick (2005). "Proposal to add Greek epigraphical letters to the UCS" (PDF). Archived from the original (PDF) on 17 February 2006. Retrieved 12 August 2010. <a href="https://web.archive.org/web/20060217000025/http://www.tlg.uci.edu/~opoudjis/unicode/epigraphical.pdf" target="_blank">https://web.archive.org/web/20060217000025/http://www.tlg.uci.edu/~opoudjis/unicode/epigraphical.pdf</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li>
<li id="fn:15"><p>Jeffery, Local Scripts of Archaic Greece, p. 89. <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li>
<li id="fn:16"><p>Thompson, Edward M. (1911). An Introduction to Greek and Latin palaeography. Oxford: Clarendon. pp. 191–194. <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li>
<li id="fn:17"><p>Weisstein, Eric W. "Epsilon". mathworld.wolfram.com. Retrieved 30 January 2025. In mathematics, a small positive infinitesimal quantity, usually denoted ε or ϵ, whose limit is usually taken as ϵ->0. <a href="https://mathworld.wolfram.com/Epsilon.html" target="_blank">https://mathworld.wolfram.com/Epsilon.html</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li>
<li id="fn:18"><p>Weisstein, Eric W. "Limit". mathworld.wolfram.com. Retrieved 30 January 2025. <a href="https://mathworld.wolfram.com/Limit.html" target="_blank">https://mathworld.wolfram.com/Limit.html</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li>
<li id="fn:19"><p>Weisstein, Eric W. "Dual Number". mathworld.wolfram.com. Retrieved 30 January 2025. <a href="https://mathworld.wolfram.com/DualNumber.html" target="_blank">https://mathworld.wolfram.com/DualNumber.html</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li>
<li id="fn:20"><p>Weisstein, Eric W. "Delta Function". mathworld.wolfram.com. Retrieved 19 February 2019. <a href="http://mathworld.wolfram.com/DeltaFunction.html" target="_blank">http://mathworld.wolfram.com/DeltaFunction.html</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li>
<li id="fn:21"><p>Überhuber, Christoph W. (1997). Numerical Computation 1: Methods, Software, and Analysis. SpringerLink Bücher. Berlin, Heidelberg: Springer. p. 140. ISBN 978-3-540-62058-7. eps frequently denotes his upper bound on the relative rounding error and is referred to as the machine epsilon. <a href="978-3-540-62058-7" target="_blank">978-3-540-62058-7</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></p></li>
<li id="fn:22"><p>"Vacuum electric permittivity". physics.nist.gov. Retrieved 10 February 2025. <a href="https://physics.nist.gov/cgi-bin/cuu/Value?ep0%7Csearch_for=universal_in!" target="_blank">https://physics.nist.gov/cgi-bin/cuu/Value?ep0%7Csearch_for=universal_in!</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></p></li>
<li id="fn:23"><p>Elert, Glenn (2023), "Special Symbols", The Physics Hypertextbook, hypertextbook, retrieved 1 February 2025, ε linear strain <a href="https://physics.info/symbols/" target="_blank">https://physics.info/symbols/</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></p></li>
<li id="fn:24"><p>Peskin, Michael E.; Schroeder, Daniel V. (4 May 2018). An Introduction To Quantum Field Theory (2nd ed.). CRC Press. ISBN 978-0-429-97210-2. <a href="978-0-429-97210-2" target="_blank">978-0-429-97210-2</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></p></li>
<li id="fn:25"><p>Montenari, Michael, ed. (2018). Cyclostratigraphy and astrochronology. Stratigraphy and Timescales (1st ed.). London San Diego, Calif. Cambridge, Mass. Oxford: Academic Press, an imprint of Elsevier. p. 84. ISBN 978-0-12-815098-6. The Earth's orbital obliquity or axial tilt (ε) is the angle between the Earth's equatorial plane and its orbital plane, <a href="978-0-12-815098-6" target="_blank">978-0-12-815098-6</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></p></li>
<li id="fn:26"><p>Free, Rhona C. (2010). 21st century economics: a reference handbook. Thousand Oaks (Calif.): Sage. pp. 93–94. ISBN 978-1-4129-6142-4. <a href="978-1-4129-6142-4" target="_blank">978-1-4129-6142-4</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></p></li>
<li id="fn:27"><p>The MATHEMATICAL symbols are used only in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style. <a href="#fnref:27" class="footnote-back-ref">↩</a></p></li>
</ol>

Epsilon open-in-new

Epsilon