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
Q.E.D. or QED is an initialism of the Latin phrase , meaning "which was to be demonstrated". Literally it states "what was to be shown". Traditionally, the abbreviation is placed at the end of mathematical proofs and philosophical arguments in p ...
''". It is inspired by the
typographic
Typography is the art and technique of typesetting, arranging type to make written language legibility, legible, readability, readable and beauty, appealing when displayed. The arrangement of type involves selecting typefaces, Point (typogra ...
practice of ''
end marks'', an element that marks the end of an article.
In
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, wh ...
, it is represented as character . Its graphic form varies, as it may be a hollow or filled rectangle or square.
In
AMS-LaTeX
AMS-LaTeX is a collection of LaTeX document classes and packages developed for the American Mathematical Society (AMS). Its additions to LaTeX include the typesetting of multi-line and other mathematical statements, document classes, and fonts c ...
, 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 ( hu, Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator ...
, who first used it in a mathematical context in 1950.
He got the idea of using it from seeing
end marks in
magazines, that is,
typographic
Typography is the art and technique of typesetting, arranging type to make written language legibility, legible, readability, readable and beauty, appealing when displayed. The arrangement of type involves selecting typefaces, Point (typogra ...
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-
-30- has been traditionally used by journalists in North America to indicate the end of a story or article that is submitted for editing and typesetting. It is commonly employed when writing on deadline and sending bits of the story at a time, v ...
*
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 th ...
*
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
Notes
References
*
{{typ-stub
Mathematical proofs
Mathematical symbols
Tombstone