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:''{{mvar|e}}'' ≈ 2,71828 18284 59045 23536 02874 71352
==Sejarah==
Referensi pertama untuk konstanta diterbitkan pada tahun 1618 dalam tabel lampiran dari sebuah karya tentang logaritma oleh [[John Napier]].<ref name="OConnor"/> Namun, semua tidak berisi konstanta itu sendiri, tetapi hanya daftar logaritma yang dihitung dari nilai konstanta. Diasumsikan bahwa tabel tersebut ditulis oleh [[William Oughtred]].
Penemuan konstanta itu sendiri dikreditkan ke [[Jacob Bernoulli]] pada tahun 1683,<ref name = "Bernoulli, 1690">Jacob Bernoulli mempertimbangkan masalah penggabungan bunga yang terus-menerus, yang menyebabkan ekspresi seri untuk ''e''. Lihat: Jacob Bernoulli (1690) "Quæstiones nonnullæ de usuris, dengan solusi problematis de sorte alearum, propositi di Efem. Empedu. 1685" (Beberapa pertanyaan tentang minat, dengan solusi masalah tentang permainan untung-untungan, diajukan di ''Journal des Savants'' (''Ephemerides Eruditorum Gallicanæ''), di tahun (anno) 1685.**), ''Acta eruditorum'', pp. 219–23. [https://books.google.com/books?id=s4pw4GyHTRcC&pg=PA222#v=onepage&q&f=false On page 222], Bernoulli mengajukan pertanyaan: ''"Alterius naturæ hoc Problema est: Quæritur, si creditor aliquis pecuniæ summam fænori exponat, ea lege, ut singulis momentis pars proportionalis usuræ annuæ sorti annumeretur; quantum ipsi finito anno debeatur?"'' (Ini adalah masalah jenis lain: Pertanyaannya adalah, apakah pemberi pinjaman akan berinvestasi [a] jumlah uang [at] bunga, biarkan terakumulasi, sehingga [at] setiap saat [it] akan menerima [a] bagian proporsional dari bunga tahunan; berapa banyak dia akan berutang [pada] akhir tahun ini?) Bernoulli menyusun deret pangkat untuk menghitung jawabannya, lalu menulis: ''" … quæ nostra serie [ekspresi matematika untuk deret geometri] &c. major est. … si ''a''=''b'', debebitur plu quam 2½''a'' & minus quam 3''a''."'' ( … which our series. … bila ''a''=''b'', [pemberi pinjaman] akan berhutang lebih dari 2½''a'' dan kurang dari 3''a''.) bila ''a''=''b'', deret geometris direduksi menjadi deret untuk ''a'' × ''e'', so 2.5 < ''e'' < 3. (** Rujukannya adalah pada masalah yang diajukan oleh Jacob Bernoulli dan yang muncul di ''Journal des Sçavans'' of 1685 at the bottom of [http://gallica.bnf.fr/ark:/12148/bpt6k56536t/f307.image.langEN page 314.])</ref><ref>{{cite book|author1=Carl Boyer|author2=Uta Merzbach|author2-link= Uta Merzbach |title=Sejarah Matematika|url=https://archive.org/details/historyofmathema00boye|url-access=registration|page=[https://archive.org/details/historyofmathema00boye/page/419 419]|publisher=Wiley|year=1991|edition=2nd}}</ref> who attempted to find the value of the following expression (which is equal to {{mvar|e}}):
:<math>\lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n.</math>
<!--The first known use of the constant, represented by the letter {{math|''b''}}, was in correspondence from [[Gottfried Leibniz]] to [[Christiaan Huygens]] in 1690 and 1691. [[Leonhard Euler]] introduced the letter {{mvar|e}} as the base for natural logarithms, writing in a letter to [[Christian Goldbach]] on 25 November 1731.<ref>Lettre XV. Euler à Goldbach, dated November 25, 1731 in: P.H. Fuss, ed., ''Correspondance Mathématique et Physique de Quelques Célèbres Géomètres du XVIIIeme Siècle'' … (Mathematical and physical correspondence of some famous geometers of the 18th century), vol. 1, (St. Petersburg, Russia: 1843), pp. 56–60, see especially [https://books.google.com/books?id=gf1OEXIQQgsC&pg=PA58#v=onepage&q&f=false p. 58.] From p. 58: ''" … ( e denotat hic numerum, cujus logarithmus hyperbolicus est = 1), … "'' ( … (e denotes that number whose hyperbolic [i.e., natural] logarithm is equal to 1) … )</ref><ref>{{Cite book|last=Remmert|first=Reinhold|authorlink=Reinhold Remmert|title=Theory of Complex Functions|page=136|publisher=[[Springer-Verlag]]|year=1991|isbn=978-0-387-97195-7}}</ref> Euler started to use the letter {{mvar|e}} for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons,<ref name="Meditatio">Euler, ''[https://scholarlycommons.pacific.edu/euler-works/853/ Meditatio in experimenta explosione tormentorum nuper instituta]''.</ref> while the first appearance of {{mvar|e}} in a publication was in Euler's ''[[Mechanica]]'' (1736).<ref>Leonhard Euler, ''Mechanica, sive Motus scientia analytice exposita'' (St. Petersburg (Petropoli), Russia: Academy of Sciences, 1736), vol. 1, Chapter 2, Corollary 11, paragraph 171, p. 68. [https://books.google.com/books?id=qalsP7uMiV4C&pg=PA68#v=onepage&q&f=false From page 68:] ''Erit enim <math>\frac{dc}{c} = \frac{dy ds}{rdx}</math> seu <math>c = e^{\int\frac{dy ds}{rdx}}</math> ubi ''e'' denotat numerum, cuius logarithmus hyperbolicus est 1.'' (So it [i.e., ''c'', the speed] will be <math>\frac{dc}{c} = \frac{dy ds}{rdx}</math> or <math>c = e^{\int\frac{dy ds}{rdx}}</math>, where ''e'' denotes the number whose hyperbolic [i.e., natural] logarithm is 1.)</ref> Although some researchers used the letter {{math|''c''}} in the subsequent years, the letter {{mvar|e}} was more common and eventually became standard.{{citation needed|date=October 2017}}
In mathematics, the standard is to typeset the constant as "{{mvar|e}}", in italics; the [[ISO 80000-2]]:2009 standard recommends typesetting constants in an upright style, but this has not been validated by the scientific community.{{citation needed|date=August 2020}}-->
== Definisi ==
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