Therefore sign
In a mathematical proof, the therefore sign (∴) is a symbol that is sometimes placed before a logical consequence, such as the conclusion of a syllogism.[citation needed] The symbol consists of three dots placed in an upright triangle and is read therefore. It is encoded at U+2234 ∴ therefore (HTML: ∴ ∴). While it is not generally used in formal writing, it is often used in mathematics and shorthand. It is complementary to U+2235 ∵ because (HTML: ∵).
Contents |
[edit] History
According to Cajori, A History of Mathematical Notations, the therefore sign was first used by Johann Rahn in 1659, in the original German edition of his book Teutsche Algebra.
[edit] Example of use
Used in a syllogism:
- All men are mortal.
- Socrates is a man.
- ∴ Socrates is mortal.
- x+1=6
- ∴ x=5
It would also be proper to indicate a premise with the because sign. For example:
∵ All men are mortals. ∵ Socrates is a man. ∴ Socrates is a mortal.
[edit] Related signs
The inverted form ∵, known as the because sign, is sometimes used as a shorthand form of "because". This is Unicode character U+2235.
The therefore sign is sometimes used as a substitute for an asterism ⁂.
To denote logical implication or entailment, various signs are used in mathematical logic: →, ⇒, ⊃, ⊢, ⊨. These symbols are then part of a mathematical formula, and are not considered to be punctuation. In contrast, the therefore sign is traditionally used as a punctuation mark, and does not form part of a formula.[1]
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 other maps the sign, often with thicker dots, is sometimes used to signal the presence of a national monument or ruins.
The character ஃ in the Tamil script represents the āytam, a special sound of the Tamil language.
In Masonic traditions the symbol is used for abbreviation, instead of the usual period. For example "R∴W∴ John Smith" is an abbreviation for "Right Worshipful John Smith" (the term Right Worshipful indicates that Brother Smith is a Grand Lodge officer).[2]
[edit] See also
[edit] References
- ^ http://www.scenta.co.uk/tcaep/maths/symbol/Mathematical%20Symbols/index.htm
- ^ Encyclopedia of Freemasonry Part 1 and Its Kindred Sciences Comprising the ..., Albert Gallatin Mackey, page 2, reprint in 2002, Kessinger Publishing, ISBN 0766126501.
