logical argument An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialecti ...

and

mathematical proof A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every pr ...

, the therefore sign, , is generally used before a

logical consequence Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is on ...

, such as the conclusion of a

syllogism A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be tru ...

. 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 Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and

shorthand Shorthand is an abbreviated symbolic writing method that increases speed and brevity of writing as compared to longhand, a more common method of writing a language. The process of writing in shorthand is called stenography, from the Greek ''s ...

History

According to Cajori, '' A History of Mathematical Notations,''

Johann Rahn Johann Rahn (Latinised form Rhonius) (10 March 1622 – 25 May 1676) was a Swiss mathematician who is credited with the first use of the division sign, ÷ (a repurposed obelus variant) and the therefore sign, ∴. The symbols were used in '' ...

used both the ''therefore'' and ''because'' signs to mean "therefore"; in the German edition of ''Teutsche Algebra'' (1659) the ''therefore'' sign was prevalent with the modern meaning, but in the 1668 English edition Rahn used the ''because'' sign 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 wasn't much in the way of consistency as to how the triangle was oriented; ''because'' with its current meaning 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 Speakers of English are also known as Anglophones, and the countries where English is natively spoken by the majority of the population are termed the ''Anglosphere''. Over two billion people speak English , making English the largest language ...

countries.

Example of use

Used in a

: :All gods are immortal. :

Zeus Zeus or , , ; grc, Δῐός, ''Diós'', label= genitive Boeotian Aeolic and Laconian grc-dor, Δεύς, Deús ; grc, Δέος, ''Déos'', label= genitive el, Δίας, ''Días'' () is the sky and thunder god in ancient Greek relig ...

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

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 ...

symbol asterism (⁂, three

asterisk The asterisk ( ), from Late Latin , from Ancient Greek , ''asteriskos'', "little star", is a typographical symbol. It is so called because it resembles a conventional image of a heraldic star. Computer scientists and mathematicians often voc ...

s) indicates moderate snow.

Freemasonry

Freemasonry Freemasonry or Masonry refers to fraternal organisations that trace their origins to the local guilds of stonemasons that, from the end of the 13th century, regulated the qualifications of stonemasons and their interaction with authorities ...

traditions, the symbol is used to indicate a Masonic abbreviation (rather than the

period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...

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 Brother Smith is a Grand Lodge officer).

Unicode

The symbol has a Unicode

code point In character encoding terminology, a code point, codepoint or code position is a numerical value that maps to a specific character. Code points usually represent a single grapheme—usually a letter, digit, punctuation mark, or whitespace—but ...

at . See

Unicode input Unicode input is the insertion of a specific Unicode character on a computer by a user; it is a common way to input characters not directly supported by a physical keyboard. Unicode characters can be produced either by selecting them from a dis ...

for keyboard-entering methods.

Similar signs

The inverted form, , known as the because sign, is sometimes used as a

form of "because". The character (visarga) in the

Tamil script The Tamil script ( , ) is an abugida script that is used by Tamils and Tamil speakers in India, Sri Lanka, Malaysia, Singapore, Indonesia and elsewhere to write the Tamil language. Certain minority languages such as Saurashtra, Badaga, ...

represents the

āytam Visarga ( sa, विसर्गः, translit=visargaḥ) means "sending forth, discharge". In Sanskrit phonology ('' ''), ' (also called, equivalently, ' by earlier grammarians) is the name of a phone voiceless glottal fricative, , written as: ...

, a special sound of the

Tamil language Tamil (; ' , ) is a Dravidian language natively spoken by the Tamil people of South Asia. Tamil is an official language of the Indian state of Tamil Nadu, the sovereign nations of Sri Lanka and Singapore, and the Indian territory o ...

. An asterism, , is a typographic symbol consisting of three

asterisks The asterisk ( ), from Late Latin , from Ancient Greek , ''asteriskos'', "little star", is a Typography, typographical symbol. It is so called because it resembles a conventional image of a star (heraldry), heraldic star. Computer scientists ...

placed in a

triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ...

. 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 Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...

to indicate 'moderate snowfall'. The graphically identical sign serves as a

Japanese map symbol This is a list of symbols appearing on Japanese maps. These symbols are called in the Japanese language. Partial list of symbols for users with visual impairment Official symbols according to the conventions of the Geographical Survey Instit ...

on the maps of the

Geographical Survey Institute of Japan The , or GSI, is the national institution responsible for surveying and mapping the national land of Japan. The former name of the organization from 1949 until March 2010 was Geographical Survey Institute; despite the rename, it retains the same ...

, 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 A national monument is a monument constructed in order to commemorate something of importance to national heritage, such as a country's founding, independence, war, or the life and death of a historical figure. The term may also refer to a spe ...

historic site A historic site or heritage site is an official location where pieces of political, military, cultural, or social history have been preserved due to their cultural heritage value. Historic sites are usually protected by law, and many have been rec ...

ruins Ruins () are the remains of a civilization's architecture. The term refers to formerly intact structures that have fallen into a state of partial or total disrepair over time due to a variety of factors, such as lack of maintenance, deliberate ...

; it has its own Unicode code point. In

Norwegian Norwegian, Norwayan, or Norsk may refer to: *Something of, from, or related to Norway, a country in northwestern Europe * Norwegians, both a nation and an ethnic group native to Norway * Demographics of Norway *The Norwegian language, including ...

and Danish, 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", ( i.e.), ( viz.) or similar.

References

{{DEFAULTSORT:Therefore Sign Typographical symbols Mathematical symbols Logic symbols Logical consequence