The Full Wiki

More info on Therefore sign

Therefore sign: Wikis

Advertisements
  

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

Encyclopedia

From Wikipedia, the free encyclopedia


Punctuation

apostrophe ( ' )
brackets ( [ ], ( ), { }, ⟨ ⟩ )
colon ( : )
comma ( , )
dashes ( , , , )
ellipses ( , ... )
exclamation mark ( ! )
full stop/period ( . )
guillemets ( « » )
hyphen ( -, )
question mark ( ? )
quotation marks ( ‘ ’, “ ” )
semicolon ( ; )
slash/stroke ( / )
solidus ( )
Word dividers
spaces ( ) () () ( ) () () ()
interpunct ( · )
General typography
ampersand ( & )
at sign ( @ )
asterisk ( * )
backslash ( \ )
bullet ( )
caret ( ^ )
copyright symbol ( © )
currency generic: ( ¤ )
specific: ฿, ¢, $, , ƒ, , , , £, , ¥, , , , , , ,
daggers ( , )
degree ( ° )
ditto mark ( )
inverted exclamation mark ( ¡ )
inverted question mark ( ¿ )
number sign/pound/hash ( # )
numero sign ( )
ordinal indicator (º, ª)
percent (etc.) ( %, ‰, )
pilcrow ( )
prime ( )
registered trademark ( ® )
section sign ( § )
service mark ( )
sound recording copyright symbol ( )
tilde ( ~ )
trademark ( )
underscore/understrike ( _ )
vertical/broken bar, pipe ( |, ¦ )
Uncommon typography
asterism ( )
falsum ( )
index/fist ( )
therefore sign ( )
because sign ( )
interrobang ( )
irony mark/percontation point ( ؟ )
lozenge ( )
reference mark ( )
tie ( )

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.

Contents

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

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 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]

Example of use

Used in a syllogism:

All humans are mortal.
Socrates is a human.
 Socrates is mortal.
x+1=6
 x=5

It Would be proper to indicate a premise with the because sign! For example:

∵ All men are mortals. ∵ Socrates is a man. ∴ Socrates is a mortal.[3]

See also

For proper Punctuation, there is another Latin phrase with a slightly different meaning, and less common in usage. Quod erat faciendum is translated as "which was to have been done". This is usually shortened to Q.E.F. The expression quod erat faciendum is a translation of the Greek geometers' closing ὅπερ ἔδει ποιῆσαι (hoper edei poiēsai). Euclid used this phrase to close propositions which were not proofs of theorems, but constructions. For example, Euclid's first proposition shows how to construct an equilateral triangle given one side.

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.
  3. ^ http://en.wikipedia.org/wiki/Talk:Therefore_sign#Because_sign_for_premise.3F
  4. ^ http://en.wikipedia.org/wiki/Q.E.D.#Q.E.F.
Advertisements

Advertisements






Got something to say? Make a comment.
Your name
Your email address
Message