# What is the name of the $\in$ symbol and where does it come from?

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?

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 $\in$).

• 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 Feb 11, 2013 at 0:52
• 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. Feb 11, 2013 at 0:59
• 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. Feb 11, 2013 at 1:06
• 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. Feb 11, 2013 at 2:06
• Whitehead and Russell's Principia Mathematica used $\epsilon$.
– MJD
Feb 12, 2013 at 0:43