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It looks like a lower-case epsilon, but the Wikipedia page on epsilon states that they are not the same.

Does this symbol have a typographic identification outside of mathematics? Where did the symbol come from?

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up vote 11 down vote accepted

This is the membership relation, but in set theory this is also known as the epsilon relation, and historically the notation was indeed $\varepsilon$.

(For example, I have the book from 1948 by Tarski and Jonsson Cardinal Algebras where such notation is employed.)

According to this page it was Peano who used epsilon. I suppose somewhere around the 1960's or so, when typography was easier to modify the symbol was taking the modern shape of $\in$ (Bourbaki in their set theory book, ca. 1970, were using $\in$).

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The symbol was introduced by Peano in volume I of his Formulaire de mathématiques from 1901 (Prémiere partie, "Logique mathématique", page 1, Chapter 1, section 1, item 4: "$x\varepsilon a$ signifie '$x$ est un $a$'."). Available here: archive.org/details/formulairedesmat00pean –  Andres Caicedo Feb 11 '13 at 0:52
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I see; nice. The difference between $\varepsilon$ and $\epsilon$ seems stylistic, though, and probably different printers chose one or the other at whim on early years. Cajori's "A history of mathematical notation", volume 2, item 689, uses $\epsilon$ and credits Peano. –  Andres Caicedo Feb 11 '13 at 0:59
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Peano's Arithmetices principia: nova methodo (1889) can be seen here: archive.org/details/arithmeticespri00peangoog The symbol here is an $\epsilon$ close to our $\in$, actually. It is introduced in page x. "Signum $\in$ significat est. Ita $a\in b$ legitur $a$ est quoddam $b$", etc. –  Andres Caicedo Feb 11 '13 at 1:06
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I read or was told early in my schooling that the epsilon was the first letter of the Greek word “is”: $\epsilon\sigma\tau\grave\iota$. The distinction between $\epsilon$ and $\varepsilon$ is merely calligraphic. –  Lubin Feb 11 '13 at 2:06
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Whitehead and Russell's Principia Mathematica used $\epsilon$. –  MJD Feb 12 '13 at 0:43

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