# Definition:Set Intersection/Historical Note

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## Historical Note on Set Intersection

The concept of **set intersection**, or **logical multiplication**, was stated by Leibniz in his initial conception of symbolic logic.

The symbol $\cap$, informally known as **cap**, was first used by Hermann Günter Grassmann in *Die Ausdehnungslehre* from $1844$.

However, he was using it as a general operation symbol, not specialized for **set intersection**.

It was Giuseppe Peano who took this symbol and used it for **intersection**, in his $1888$ work *Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann*.

Peano also created the large symbol $\bigcap$ for general intersection of more than two sets.

This appeared in his *Formulario Mathematico, 5th ed.* of $1908$.

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.19$: Leibniz ($\text {1646}$ – $\text {1716}$)

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