Therefore sign

Therefore sign

In a mathematical proof, the "therefore" sign (Unicode|∴) is a symbol that is sometimes placed before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in a triangle. In reading, it is pronounced "Therefore, …". It is Unicode character U+2234. While it is not generally used in formal writing, it is often used in mathematics and shorthand.

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".

Related signs

The inverted form Unicode|∵, 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 [Unicode|⁂] .

To denote logical implication or entailment, various signs are used in mathematical logic: Unicode|→, Unicode|⇒, Unicode|⊃, Unicode|⊢, Unicode|⊨. 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.

To denote a cultural or historical site (such as a ruin) on a map. Japan: National Monument [http://en.wikipedia.org/wiki/Japanese_map_symbols]

Examples

Used in a syllogism:

:All humans are mortal.:Socrates is a human.:Unicode|∴ Socrates is mortal.

In secret societies

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."Encyclopedia of Freemasonry Part 1 and Its Kindred Sciences Comprising the ...", Albert Gallatin Mackey, page 2, reprint in 2002, Kessinger Publishing, ISBN 0766126501.]

imilar symbols

*The Āytham is a special sound of Tamil represented by Unicode|ஃ in the Tamil script.

ee also

*Q.E.D.

References


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