Therefore sign

From Wikipedia, the free encyclopedia

∴ 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

[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

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]

[edit] Examples

Used in a syllogism:

All humans are mortal.

Socrates is a human.

∴ Socrates is mortal.

[edit] 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]

[edit] Similar symbols

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

[edit] See also

• Q.E.D.

[edit] 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.