Tombstone (typography)

# Tombstone (typography)

Discussion

Encyclopedia
The tombstone, halmos, or end of proof mark "" is used in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

to denote the end of a proof
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...

, in place of the traditional abbreviation "QED" for the Latin phrase "quod erat demonstrandum
Q.E.D.
Q.E.D. is an initialism of the Latin phrase , which translates as "which was to be demonstrated". The phrase is traditionally placed in its abbreviated form at the end of a mathematical proof or philosophical argument when what was specified in the enunciation — and in the setting-out —...

" (Q.E.D.).

In Unicode
Unicode
Unicode is a computing industry standard for the consistent encoding, representation and handling of text expressed in most of the world's writing systems...

, 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
AMS-LaTeX
AMS-LaTeX is a collection ofLaTeX document classes and packages developed for the American Mathematical Society . Its additions to LaTeX include the typesetting of multi-line and other mathematical statements, document classes, and fonts containing numerous mathematical symbols.It has largely...

, 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
Eponym
An eponym is the name of a person or thing, whether real or fictitious, after which a particular place, tribe, era, discovery, or other item is named or thought to be named...

Paul Halmos
Paul Halmos
Paul Richard Halmos was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis . He was also recognized as a great mathematical expositor.-Career:Halmos obtained his B.A...

, who first used it in mathematical context, after seeing it was being used to indicate the end of articles in magazine
Magazine
Magazines, periodicals, glossies or serials are publications, generally published on a regular schedule, containing a variety of articles. They are generally financed by advertising, by a purchase price, by pre-paid magazine subscriptions, or all three...

s.

• Bourbaki dangerous bend symbol
Bourbaki dangerous bend symbol
The dangerous bend or caution symbol ☡ was created by the Nicolas Bourbaki group of mathematicians and appears in the margins of mathematics books written by the group...

• End-of-file
End-of-file
In computing, end of file is a condition in a computer operating system where no more data can be read from a data source...

• End-of-transmission character
End-of-transmission character
In telecommunication, an end-of-transmission character is a transmission control character. Its intended use is to indicate the conclusion of a transmission that may have included one or more texts and any associated message headings....

• Q.E.D.
Q.E.D.
Q.E.D. is an initialism of the Latin phrase , which translates as "which was to be demonstrated". The phrase is traditionally placed in its abbreviated form at the end of a mathematical proof or philosophical argument when what was specified in the enunciation — and in the setting-out —...