Therefore sign

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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 Unicode character U+2234 and on some systems may be entered using ALT-8756 (the decimal version of 2234). While it is not generally used in formal writing, it is often used in mathematics and shorthand.

[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] Related signs

A diploma from the Masonic Grande Loge de France showing the symbol as a substitute for the dot of abbreviation.

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.

Some secret traditions use this sign for abbreviation instead of the usual period. This usage is much more frequent in French Freemasonry than in the English one.^[2]

[edit] Example of use

Used in a syllogism:

All humans are mortal.

Socrates is a human.

∴ Socrates is mortal.

x+1=6

∴ x=5

[edit] See also

• Q.E.D.

[edit] References

1. ^ http://www.scenta.co.uk/tcaep/maths/symbol/Mathematical%20Symbols/index.htm
2. ^ Encyclopedia of Freemasonry Part 1 and Its Kindred Sciences Comprising the ..., Albert Gallatin Mackey, page 2, reprint in 2002, Kessinger Publishing, ISBN 0766126501.