In Argument and mathematical proof, the therefore sign, , is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore. While it is not generally used in formal writing, it is used in mathematics and shorthand.
History
According to
Florian Cajori in
A History of Mathematical Notations, the Swiss mathematician
Johann Rahn used both an upright and an inverted triangle of dots to mean
therefore. In the German edition of
Teutsche Algebra (1659), he used the upright triangle with its modern meaning, but in the 1668 English edition Rahn used the inverted triangle more often to mean 'therefore'. Other authors in the 18th century also used three dots in a triangle shape to signify 'therefore', but as with Rahn, there was little consistency as to how the triangle was oriented. Use of an upright triangle exclusively to mean
therefore (and an inverted
triangle exclusively to mean
because) appears to have originated in the 19th century. In the 20th century, the three-dot notation for 'therefore' became very rare in continental Europe, but it remains popular in
Anglophone countries.
Examples of use
Used in a
syllogism:
- All gods are immortal.
- Zeus is a god.
- ∴ Zeus is immortal.
and in mathematics:
Other uses
In meteorology, the therefore sign is used to indicate "moderate rain" on a
station model; the similar
typography symbol asterism (⁂, three
) indicates moderate snow.
Freemasonry
In
Freemasonry and certain related traditions, the symbol is used to indicate a Masonic abbreviation (rather than the
full stop mark used conventionally with some abbreviations). For example, "R∴W∴ John Smith" is an abbreviation for "Right Worshipful John Smith" (the term
Right Worshipful is an honorific and indicates that Smith is a
Grand Lodge officer).
Unicode
The symbol has a Unicode
code point at . See
Unicode input for keyboard-entering methods.
LaTeX
One can write the symbol in
LaTeX by using the amssymb package with the \therefore command.
Similar signs
The inverted form,
, known as the
because sign, is sometimes used as a
shorthand form of "because".
The character (visarga) in the Tamil script represents the āytam, a special sound of the Tamil language.
An asterism, , is a typographic symbol consisting of three asterisks () placed in a triangle. Its purpose is to "indicate minor breaks in text", to call attention to a passage, or to separate sub-chapters in a book. It is also used in meteorology to indicate 'moderate snowfall'.
The graphically identical sign serves as a Japanese map symbol on the maps of the Geographical Survey Institute of Japan, indicating a tea plantation. On some maps, a version of the sign with thicker dots, , is used to signal the presence of a national monument, historic site or ruins; it has its own Unicode code point.
In Norwegian and Danish language, a superficially similar symbol was formerly used as an explanatory symbol ( forklaringstegnet). It can be typeset using the open o followed by a colon, thus: . It is used for the meaning "namely", id est (i.e.), videlicet (viz.) or similar.
See also
-
Q.E.D.
-
List of mathematical jargon
