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Therefore sign

∴ v • d • e Punctuation
apostrophe ( ’ ' ) brackets (( )), ([ ]), ({ }), (< >) colon ( : ) comma ( , ) dashes ( ‒, –, —, ― ) ellipsis ( …, ... ) exclamation mark ( ! ) full stop/period ( . ) guillemets ( « » ) hyphen ( -, ‐ ) question mark ( ? ) quotation marks ( ‘ ’, “ ” ) semicolon ( ; ) slash/stroke ( / ) solidus ( ⁄ )
Interword separation
spaces ( ) ( ) ( ) interpunct ( · )
General typography
ampersand ( & ) at sign ( @ ) asterisk ( * ) backslash ( \ ) bullet ( • ) caret ( ^ ) currency ( ¤ ) ¢, $, €, £, ¥, ₩, ₪ dagger/obelisk ( † ) ( ‡ ) degree ( ° ) inverted exclamation point ( ¡ ) inverted question mark ( ¿ ) not sign ( ¬ ) number sign ( # ) numero sign ( № ) percent and related signs ( %, ‰, ‱ ) pilcrow ( ¶ ) prime ( ′ ) section sign ( § ) tilde/swung dash ( ~ ) umlaut/diaeresis ( ¨ ) underscore/understrike ( _ ) vertical/pipe/broken bar ( |, ¦ )
Uncommon typography
asterism ( ⁂ ) index/fist ( ☞ ) therefore sign ( ∴ ) interrobang ( ‽ ) irony mark ( ؟ ) reference mark ( ※ ) sarcasm mark

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. 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.

Contents 1 History 2 Related signs 3 Examples 4 In secret societies 5 Similar symbols 6 See also 7 References

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 ∵, 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.

To denote a cultural or historical site (such as a ruin) on a map. Japan: National Monument [1]

Examples

Used in a syllogism:

All humans are mortal.

Socrates is a human.

∴ 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.^[1]

Similar symbols

• The Āytham is a special sound of Tamil represented by ஃ in the Tamil script.

See also

• Q.E.D.

References

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