Tombstone (typography)

The tombstone, halmos, or end of proof mark "∎" is used in mathematics to denote the end of a proof, in place of the traditional abbreviation "QED" for the Latin phrase "quod erat demonstrandum" (Q.E.D.).

In Unicode, it is represented as character U+220E "End of Proof". Its graphic form varies. 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 or \qed (the latter causes the symbol to be right aligned).

It is sometimes called a halmos after its eponym Paul Halmos, who first used it in mathematical context, after seeing it was being used to indicate the end of articles in magazines.^[1]

See also

• Bourbaki dangerous bend symbol
• End-of-file
• End-of-transmission character
• Q.E.D.

Notes

1. ^ "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'.", 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, http://jeff560.tripod.com/set.html, retrieved June 26, 2010