# Definition:Element/Historical Note

## Historical Note on Element

The symbol for **is an element of ** originated as $\varepsilon$, first used by Giuseppe Peano in his *Arithmetices prinicipia nova methodo exposita* of $1889$. It comes from the first letter of the Greek word meaning **is**.

The stylized version $\in$ was first used by Bertrand Russell in *Principles of Mathematics* in $1903$.

See Earliest Uses of Symbols of Set Theory and Logic in Jeff Miller's website Earliest Uses of Various Mathematical Symbols.

$x \mathop \varepsilon S$ could still be seen in works as late as 1951: Nathan Jacobson: *Lectures in Abstract Algebra: Volume $\text { I }$: Basic Concepts* and 1955: John L. Kelley: *General Topology*.

Paul Halmos wrote in *Naive Set Theory* in $1960$ that:

*This version [$\epsilon$] of the Greek letter epsilon is so often used to denote belonging that its use to denote anything else is almost prohibited. Most authors relegate $\epsilon$ to its set-theoretic use forever and use $\varepsilon$ when they need the fifth letter of the Greek alphabet.*

However, since then the symbol $\in$ has been developed in such a style as to be easily distinguishable from $\epsilon$, and by the end of the $1960$s the contemporary notation was practically universal.

## Sources

- 1960: Paul R. Halmos:
*Naive Set Theory*... (previous) ... (next): $\S 1$: The Axiom of Extension

- 1963: George F. Simmons:
*Introduction to Topology and Modern Analysis*... (previous) ... (next): $\S 1$: Sets and Set Inclusion - 2008: Paul Halmos and Steven Givant:
*Introduction to Boolean Algebras*... (previous) ... (next): Appendix $\text{A}$: Set Theory: Sets and Subsets - 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (previous) ... (next): Appendix $\text{A}.1$: Definition $\text{A}.1$