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In logical 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, Johann Rahn 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".: vol. 1, p. 211 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; 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 countries.
Examples of use
Used in a syllogism:
All gods are immortal.
Zeus is a god.
∴ Zeus is immortal.
and in mathematics:
x + 1 = 10
∴ x = 9
Other uses
In meteorology, the therefore sign is used to indicate "moderate rain" on a station model; the similar typographic symbol asterism (⁂, three asterisks) indicates moderate snow.
= Freemasonry
=
In Freemasonry traditions, the symbol is used to indicate a Masonic abbreviation (rather than the period 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 U+2234 ∴ THEREFORE (∴, ∴, ∴). See Unicode input for keyboard-entering methods.
Similar signs
The inverted form, ∵, known as the because sign, is sometimes used as a shorthand form of "because".
The character ஃ (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, 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: ɔ:. It is used for the meaning "namely", id est (i.e.), scilicet (viz.) or similar.
See also
Q.E.D.
List of mathematical jargon
References
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In contrast, the therefore sign [∴] is traditionally used as a punctuation mark, and does not form part of a formula. It also refers to the "complementary" of the "therefore" symbol ∴, namely the symbol ∵, which denotes "because".
I've recently read a book which used the sign ∴ ∴ (for "therefore"). It was more or less clear from the context what was meant, but I looked it up among the AMS LaTeX symbols just to be sure. They also listed the similar ∵ ∵ ("because") sign. I might have seen this notation before, but very rarely if at all. Is this because I've studied in Germany and these symbols are used more often ...
26 Des 2015 · Question: I recently read the symbol $\\therefore$ in a couple of posts. Unfortunately i can't find the posts anymore. Does this have any special mathematical meaning?
09 Jul 2020 · The logical sign ∴ , known as the Therefore sign and also read therefore, generally used before a logical consequence, such as the conclusion of a syllogism. For example, (a) All humans are mortal. Socrates is a human. ∴ Socrates is mortal. (b) x + 1 = 10 ∴ x = 9 On the other hand, the logical sign ⊢ , known as the Turnstile and read as provable, stands for …
29 Mar 2023 · When writing mathematical proof we will commonly use 3 dots in a triangular arrangement as shorthand for therefore. Is there a reason this symbol is used or was it just decided my someone a long time ago?
12 Mei 2016 · The symbol means "therefore". In common usage, "therefore" is a stronger statement than "if/then". When we say " p p therefore q q ", we mean both "if p p then q q " and " p p is true". Thus we assure that q q is true, which the "if/then" statement alone does not. Mathematically: p ∴ q ≡ ((p → q) ∧ p) p ∴ q ≡ ((p → q) ∧ p)
14 Apr 2017 · The inverted form of the therefore sign ( ∴ ∴ ) used in proofs before logical consequences, is known as the because sign ( ∵ ∵ ) and it is used in proofs before reasoning.
03 Mar 2019 · Whats the meaning of this symbol? Its a three dot symbol: ∴ I read a book, im could not find any definition of this symbol. This is about continuum property of the natural numbers and the archimed...
What does the $\\Rightarrow$ arrow mean when showing working out in maths? How do we use it appropriately?
27 Jul 2017 · What does the symbol $$/\\therefore$$ mean in sentential logic? I know that $\\therefore$ denotes the conclusion of an argument. Does $/\\therefore$ mean not follows? Thanks in advance for any help!
