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Therefore sign

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Therefore sign

Therefore sign
Punctuation
apostrophe ( ’ ' )
brackets ( [ ], ( ), { }, ⟨ ⟩ )
colon ( : )
comma ( , ، 、 )
dash ( , –, —, ― )
ellipsis ( …, ..., . . . )
exclamation mark ( ! )
full stop / period ( . )
hyphen ( )
hyphen-minus ( - )
question mark ( ? )
quotation marks ( ‘ ’, “ ”, ' ', " " )
semicolon ( ; )
slash / stroke / solidus ( /,  ⁄  )
Word dividers
interpunct ( · )
space ( ) ( ) ( )
General typography
ampersand ( & )
asterisk ( * )
at sign ( @ )
backslash ( \ )
bullet ( )
caret ( ^ )
dagger ( †, ‡ )
degree ( ° )
ditto mark ( )
inverted exclamation mark ( ¡ )
inverted question mark ( ¿ )
number sign / pound / hash ( # )
numero sign ( )
obelus ( ÷ )
ordinal indicator ( º, ª )
percent, per mil ( %, ‰ )
plus and minus ( + − )
basis point ( )
pilcrow ( )
prime ( ′, ″, ‴ )
section sign ( § )
tilde ( ~ )
underscore / understrike ( _ )
vertical bar / broken bar / pipe ( ¦, | )
Intellectual property
copyright symbol ( © )
registered trademark ( ® )
service mark ( )
sound recording copyright ( )
trademark ( )
Currency
currency (generic) ( ¤ )
currency (specific)
( ฿ ¢ $ ƒ £ ¥ )
Uncommon typography
asterism ( )
hedera ( )
index / fist ( )
interrobang ( )
irony punctuation ( )
lozenge ( )
reference mark ( )
tie ( )
Related
diacritical marks
logic symbols
whitespace characters
non-English quotation style ( « », „ ” )
In other scripts
Chinese punctuation
Hebrew punctuation
Japanese punctuation
Korean punctuation

In mathematical proof, the therefore sign (∴) is sometimes placed before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore. It is encoded at U+2234 therefore (HTML: ). While it is not generally used in formal writing, it is often used in mathematics and shorthand. It is complementary to U+2235 because (HTML: ).

History

According to Cajori, A History of Mathematical Notations, Johann Rahn used both the therefore and because signs to mean "therefore"; in the German edition of Teutsche Algebra (1659) the therefore sign was prevalent with the modern meaning, but in the 1668 English edition Rahn used the because sign more often to mean "therefore".[1] Other authors in the eighteenth century also used three dots in a triangle shape to signify "therefore", but as with Rahn, there wasn't much in the way of consistency as to how the triangle was oriented; because with its current meaning appears to have originated in the nineteenth century. Also, in this century, the three-dot notation for therefore becomes very rare in continental Europe, but remains popular in the British Isles.[2]

Example of use

Used in a syllogism:

All gods are immortal.
Zeus is a god.
 Zeus is immortal.
x+1=6
 x=5

It would also be proper to indicate a premise with the because sign. For example:

∵ All gods are immortals. ∵ Zeus is a god. ∴ Zeus is an immortal.

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.[3]

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.

In Masonic traditions the symbol is used for abbreviation, instead of the usual period. For example "R∴W∴ John Smith" is an abbreviation for "Right Worshipful John Smith" (the term Right Worshipful indicates that Brother Smith is a Grand Lodge officer).[4]

See also

References

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