In mathematics, the **tombstone**, **halmos**, **end-of-proof**, or **Q.E.D.** symbol "∎" (or "□") is a symbol used to denote the end of a proof, in place of the traditional abbreviation "Q.E.D." for the Latin phrase "*quod erat demonstrandum*", meaning "which was to be demonstrated".^{[1]} In magazines, it is one of the various symbols used to indicate the end of an article.^{[2]}

In Unicode, it is represented as character U+220E ∎ END OF PROOF (HTML `∎`

). Its graphic form varies, as it may be a hollow or filled rectangle or square.

In AMS-LaTeX, the symbol is automatically appended at the end of a proof environment `\begin{proof}` ... `\end{proof}`. It can also be obtained from the commands `\qedsymbol`, `\qedhere`

or `\qed` (the latter causes the symbol to be right aligned).^{[3]}

It is sometimes called a "Halmos finality symbol" or "halmos" after the mathematician Paul Halmos, who first used it in a mathematical context in 1950.^{[4]} He got the idea of using it from seeing it was being used to indicate the end of articles in magazines. In his memoir *I Want to Be a Mathematician*, he wrote the following:^{[5]}

The symbol is definitely not my invention — it appeared in popular magazines (not mathematical ones) before I adopted it, but, once again, I seem to have introduced it into mathematics. It is the symbol that sometimes looks like ▯, and is used to indicate an end, usually the end of a proof. It is most frequently called the 'tombstone', but at least one generous author referred to it as the 'halmos'.

## See also

## Notes

**^**"The Definitive Glossary of Higher Mathematical Jargon — Q.E.D."*Math Vault*. 2019-08-01. Retrieved 2019-11-04.**^**Foster, A. J. "Tombstones in Typography | AJ Foster".*aj-foster.com*. Retrieved 2019-11-05.**^**"LaTeX/Theorems - Wikibooks, open books for an open world".*en.wikibooks.org*. Retrieved 2019-11-05.**^**Halmos, Paul R. (Paul Richard), 1916-2006. (1950).*Measure theory*. New York: Van Nostrand. pp. 6. ISBN 0387900888. OCLC 529634.CS1 maint: multiple names: authors list (link)**^**Paul R. Halmos,*I Want to Be a Mathematician: An Automathography*, 1985, p. 403.

## References

- Miller, Jeff (September 29, 2007),
*Earliest Uses of Symbols of Set Theory and Logic*, retrieved June 26, 2010

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