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", "which had to be demonstrated" (Q.E.D.). In magazines, it is one of the various symbols used to indicate the end of an article.

In Unicode, it is represented as character U+220E ∎ end of proof (HTML ∎). 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 the mathematician Paul Halmos, who first used it in mathematical context. 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:[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’. ”

See also

Notes

  1. ↑ Paul R. Halmos, I Want to Be a Mathematician: An Automathography, 1985, p. 403.

References