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
Proof most often refers to:
* Proof (truth), argument or sufficient evidence for the truth of a proposition
* Alcohol proof, a measure of an alcoholic drink's strength
Proof may also refer to:
Mathematics and formal logic
* Formal proof, a co ...
, in place of the traditional abbreviation "Q.E.D." for the Latin phrase "''
quod erat demonstrandum''". It is inspired by the
typographic practice of ''
end marks'', an element that marks the end of an article.
In
Unicode
Unicode or ''The Unicode Standard'' or TUS is a character encoding standard maintained by the Unicode Consortium designed to support the use of text in all of the world's writing systems that can be digitized. Version 16.0 defines 154,998 Char ...
, it is represented as character . 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 ...
\end. It can also be obtained from the commands
\qedsymbol,
\qedhere or
\qed (the latter causes the symbol to be right aligned).
It is sometimes called a "Halmos finality symbol" or "halmos" after the mathematician
Paul Halmos
Paul Richard Halmos (; 3 March 1916 – 2 October 2006) was a Kingdom of Hungary, Hungarian-born United States, American mathematician and probabilist who made fundamental advances in the areas of mathematical logic, probability theory, operat ...
, who first used it in a mathematical context in 1950.
He got the idea of using it from seeing
end marks in
magazine
A magazine is a periodical literature, periodical publication, print or digital, produced on a regular schedule, that contains any of a variety of subject-oriented textual and visual content (media), content forms. Magazines are generally fin ...
s, that is,
typographic signs that indicate the end of an article. In his memoir ''I Want to Be a Mathematician'', he wrote the following:
[Paul R. Halmos, ]
I Want to Be a Mathematician: An Automathography
', 1985, p. 403.
See also
*
-30-
*
Block Elements
Block Elements is a Unicode block containing square block symbols of various fill and shading. Used along with block elements are box-drawing characters, shade characters, and terminal graphic characters. These can be used for filling regions of t ...
*
End-of-file
In computing, end-of-file (EOF) is a condition in a computer operating system where no more data can be read from a data source. The data source is usually called a file or stream.
Details
In the C standard library, the character-reading functi ...
*
End-of-Transmission character
In telecommunications, an End-of-Transmission character (EOT) is a transmission (telecommunications), transmission control character. Its intended use is to indicate the conclusion of a transmission that may have included one or more texts and an ...
*
Therefore sign (∴)
Notes
References
*
{{typ-stub
Mathematical proofs
Mathematical symbols
Tombstone
A gravestone or tombstone is a marker, usually stone, that is placed over a grave. A marker set at the head of the grave may be called a headstone. An especially old or elaborate stone slab may be called a funeral stele, stela, or slab. The us ...