Therefore sign
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∴
Therefore sign
Punctuation
apostrophe ’ '
brackets [ ] ( ) { } ⟨ ⟩
colon :
comma , ، 、
dash ‒ – — ―
ellipsis … ... ⋯ ᠁ ฯ
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General typography
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degree °
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komejirushi, kome, reference mark ※
number sign, pound, hash #
numero sign №
obelus ÷
multiplication sign ×
ordinal indicator º ª
percent, per mil % ‰
plus and minus + −
equals sign =
basis point ‱
pilcrow ¶
prime ′ ″ ‴
section sign §
tilde ~
underscore, understrike _
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currency symbols
؋ ​₳ ​ ฿ ​₿ ​ ₵ ​¢ ​₡ ​₢ ​ $ ​₫ ​₯ ​֏ ​ ₠ ​€ ​ ƒ ​₣ ​ ₲ ​ ₴ ​ ₭ ​ ₺ ​₾ ​ ₼ ​ℳ ​₥ ​ ₦ ​ ₧ ​₱ ​₰ ​£ ​ 元 圆 圓 ​﷼ ​៛ ​₽ ​₹ ₨ ​ ₪ ​ ৳ ​₸ ​₮ ​ ₩ ​ ¥ 円
Uncommon typography
asterism ⁂
fleuron, hedera ❧
index, fist ☞
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In logical argument and mathematical proof, the therefore sign (∴) is generally used 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 &#8756; · &there4;). For common use in Microsoft Office hold the ALT key and type "8756". While it is not generally used in formal writing, it is used in mathematics and shorthand. It is complementary to U+2235 ∵ because (HTML &#8757;).
Contents
[hide]
1 History
2 Example of use
3 Related signs
4 See also
5 References
History[edit]
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. In this century, the three-dot notation for therefore became very rare in continental Europe, but it remains popular in the British Isles.[2]
Example of use[edit]
Used in a syllogism:
All gods are immortal.
Zeus is a god.
∴ Zeus is immortal.
x + 1 = 6
∴ x = 5
Related signs[edit]
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 ⁂.
In meteorology, the therefore sign is used to indicate moderate rain on a station model; the asterism indicates moderate snow.
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 logical 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 ஃ 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 is an archaic title just as "Land Lord" is and indicates that Brother Smith is a Grand Lodge officer).[4]
In Norwegian and Danish, a similar symbol is used as an explanatory symbol (forklaringstegnet). It can be typeset using the open o followed by a colon, thus: ɔ:. It is used for the meaning "namely", "id est", "scilicet" or similar[5].
See also[edit]
Q.E.D.
Mathematical jargon
References[edit]
Jump up ^ "Cajori, vol. 1, p. 211". Archive.org. Retrieved 2013-10-05.
Jump up ^ Florian Cajori (2011) [1929]. A History of Mathematical Notations: Two Volumes in One. Cosimo, Inc. pp. 282–283. ISBN 978-1-61640-571-7.
Jump up ^ [1] Archived October 14, 2008, at the Wayback Machine.
Jump up ^ Encyclopedia of Freemasonry Part 1 and Its Kindred Sciences Comprising the ..., Albert Gallatin Mackey, page 2, reprint in 2002, Kessinger Publishing, ISBN 0-7661-2650-1.
Jump up ^ http://www.typografi.org/forklaringstegn/forklaringstegn.html
[hide]
v
t
e
Common logical symbols
∧ or &
and
∨
or
¬ or ~
not
→
implies
⊃
implies,
superset
≡
iff
|
nand
∀
universal
quantification
∃
existential
quantification
⊤
tautology
⊥
false,
contradiction
⊢
entails,
proves
⊨
entails,
therefore
∴
therefore
∵
because
Retrieved from "https://en.wikipedia.org/w/index.php?title=Therefore_sign&oldid=815234923"
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text-align:right;font-size:125%;line-height:0.8em;vertical-align:middle;white-space:nowrap;
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a
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nowrap
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span
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nowrap
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/wiki/Intellectual_property Intellectual property
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text-align:right;font-size:125%;line-height:0.8em;vertical-align:middle;white-space:nowrap;
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a
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/wiki/Sound_recording_copyright_symbol Sound recording copyright symbol
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text-align:right;font-size:125%;line-height:0.8em;vertical-align:middle;white-space:nowrap;
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/wiki/Afghan_afghani Afghan afghani
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/wiki/Argentine_austral Argentine austral
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/wiki/Thai_baht Thai baht
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/wiki/Bitcoin Bitcoin
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/wiki/Costa_Rican_col%C3%B3n Costa Rican colón
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/wiki/Brazilian_cruzeiro Brazilian cruzeiro
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/wiki/Dollar_sign Dollar sign
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/wiki/Greek_drachma Greek drachma
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/wiki/Armenian_dram_sign Armenian dram sign
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/wiki/European_Currency_Unit European Currency Unit
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/wiki/Euro_sign Euro sign
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/wiki/Paraguayan_guaran%C3%AD Paraguayan guaraní
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/wiki/Hryvnia_sign Hryvnia sign
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/wiki/Lao_kip Lao kip
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/wiki/Turkish_lira_sign Turkish lira sign
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/wiki/Georgian_Lari mw-redirect Georgian Lari
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/wiki/Azerbaijani_manat Azerbaijani manat
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/wiki/German_gold_mark German gold mark
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/wiki/Mill_(currency) Mill (currency)
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/wiki/Nigerian_naira Nigerian naira
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/wiki/Pfennig Pfennig
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/wiki/Pound_sign Pound sign
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/wiki/Renminbi Renminbi
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/wiki/Iranian_rial Iranian rial
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/wiki/Kazakhstani_tenge Kazakhstani tenge
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/wiki/Mongolian_t%C3%B6gr%C3%B6g Mongolian tögrög
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/wiki/Won_sign Won sign
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/wiki/Japanese_yen Japanese yen
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p
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div
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wrap nounderlines max-width:17.5em; line-height:1.1em; padding-left:1em;
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colspan style
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tr
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a
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/wiki/Asterism_(typography) Asterism (typography)
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text-align:right;font-size:125%;line-height:0.8em;vertical-align:middle;white-space:nowrap;
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/wiki/Irony_punctuation Irony punctuation
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href title
/wiki/Lozenge Lozenge
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a
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/wiki/Tie_(typography) Tie (typography)
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text-align:left;
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span
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position: relative; top: 0.25em;
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tbody
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table
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width:100%;border-collapse:collapse;border-spacing:0px 0px;border:none;line-height:1.3em;
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td
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2 text-align:center
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noprint
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colspan style
2 text-align:center;background:#e0e0e0;padding:0.15em;padding-left:0.3em;
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tr
class
noprint
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a
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/wiki/Diacritic Diacritic
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a
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/wiki/List_of_logic_symbols List of logic symbols
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ul
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hlist hlist-separated
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/wiki/Whitespace_character Whitespace character
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ul
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plainlist
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/wiki/Writing_system Writing system
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tr
class
noprint
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a
href title
/wiki/Chinese_punctuation Chinese punctuation
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li
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a
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/wiki/Hebrew_punctuation Hebrew punctuation
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li
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a
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/wiki/Japanese_punctuation Japanese punctuation
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li
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a
href title
/wiki/Korean_punctuation Korean punctuation
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li
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ul
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div
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html
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colspan style
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class
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local
img
alt src title width height srcset data-file-width data-file-height
Category //upload.wikimedia.org/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/16px-Folder_Hexagonal_Icon.svg.png Category 16 14 //upload.wikimedia.org/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/24px-Folder_Hexagonal_Icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/32px-Folder_Hexagonal_Icon.svg.png 2x 36 31
html
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a
href title
/wiki/Category:Typographical_symbols Category:Typographical symbols
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li
html
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img
alt src title width height srcset data-file-width data-file-height
Portal //upload.wikimedia.org/wikipedia/en/thumb/f/fd/Portal-puzzle.svg/16px-Portal-puzzle.svg.png Portal 16 14 //upload.wikimedia.org/wikipedia/en/thumb/f/fd/Portal-puzzle.svg/24px-Portal-puzzle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/fd/Portal-puzzle.svg/32px-Portal-puzzle.svg.png 2x 32 28
html
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a
href title
/wiki/Portal:Typography Portal:Typography
html
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li
html
local
ul
html
local
img
alt src title width height srcset data-file-width data-file-height
Wikipedia book //upload.wikimedia.org/wikipedia/commons/thumb/8/89/Symbol_book_class2.svg/16px-Symbol_book_class2.svg.png Wikipedia book 16 16 //upload.wikimedia.org/wikipedia/commons/thumb/8/89/Symbol_book_class2.svg/23px-Symbol_book_class2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/89/Symbol_book_class2.svg/31px-Symbol_book_class2.svg.png 2x 180 185
html
local
a
href title
/wiki/Book:Typographical_symbols Book:Typographical symbols
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li
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ul
html
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td
colspan class style
2 hlist noprint text-align:center;background:#e0e0e0;padding:0.25em 0.25em 0.4em;line-height:1.75em;font-weight:bold;
html
local
tr
html
local
abbr
title
View this template
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local
a
href title
/wiki/Template:Punctuation_marks Template:Punctuation marks
html
local
li
class
nv-view
html
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abbr
title
Discuss this template
html
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a
href title
/wiki/Template_talk:Punctuation_marks Template talk:Punctuation marks
html
local
li
class
nv-talk
html
local
abbr
title
Edit this template
html
local
a
class href
external text //en.wikipedia.org/w/index.php?title=Template:Punctuation_marks&action=edit
html
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li
class
nv-edit
html
local
ul
html
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div
class
plainlinks hlist navbar mini
html
local
td
colspan style
2 text-align:right
html
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tr
html
local
tbody
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table
class style
infobox width:22em;width:18em; max-width:18em;
html
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a
href title
/wiki/Argument Argument
html
local
a
href title
/wiki/Mathematical_proof Mathematical proof
html
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b
html
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a
href title
/wiki/Logical_consequence Logical consequence
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a
href title
/wiki/Syllogism Syllogism
html
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i
html
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span
class style
monospaced font-family: monospace, monospace;
html
local
span
class
nowrap
html
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span
style
font-size:125%
html
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span
class style
smallcaps font-variant: small-caps; font-size: smaller;
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code
html
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b
html
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code
html
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a
href title
/wiki/Mathematics Mathematics
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a
href title
/wiki/Shorthand Shorthand
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span
class style
monospaced font-family: monospace, monospace;
html
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span
class
nowrap
html
local
span
style
font-size:125%
html
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span
class style
smallcaps font-variant: small-caps; font-size: smaller;
html
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code
html
local
p
html
local
p
html
local
h2
html
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a
role tabindex class
button 0 togglelink
html
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span
class
toctoggle
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div
class dir xml:lang
toctitle ltr en
html
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span
class
tocnumber
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span
class
toctext
html
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a
href
#History
html
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li
class
toclevel-1 tocsection-1
html
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span
class
tocnumber
html
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span
class
toctext
html
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a
href
#Example_of_use
html
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li
class
toclevel-1 tocsection-2
html
local
span
class
tocnumber
html
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span
class
toctext
html
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a
href
#Related_signs
html
local
li
class
toclevel-1 tocsection-3
html
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span
class
tocnumber
html
local
span
class
toctext
html
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a
href
#See_also
html
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li
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toclevel-1 tocsection-4
html
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span
class
tocnumber
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class
toctext
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a
href
#References
html
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li
class
toclevel-1 tocsection-5
html
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ul
html
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div
id class
toc toc
html
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p
html
local
span
class id
mw-headline History
html
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span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Therefore_sign&action=edit&section=1 Edit section: History
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href title
/wiki/Florian_Cajori Florian Cajori
html
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i
html
local
a
href title
/wiki/Johann_Rahn Johann Rahn
html
local
i
html
local
i
html
local
i
html
local
i
html
local
i
html
local
a
href
#cite_note-1
html
local
sup
id class
cite_ref-1 reference
html
local
i
html
local
a
href
#cite_note-Cajori2011-2
html
local
sup
id class
cite_ref-Cajori2011_2-0 reference
html
local
p
html
local
span
class id
mw-headline Example_of_use
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Therefore_sign&action=edit&section=2 Edit section: Example of use
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
a
href title
/wiki/Syllogism Syllogism
html
local
p
html
local
dd
html
local
a
href title
/wiki/Zeus Zeus
html
local
dd
html
local
dd
html
local
dl
html
local
dd
html
local
dd
html
local
dl
html
local
span
class id
mw-headline Related_signs
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Therefore_sign&action=edit&section=3 Edit section: Related signs
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
local
img
alt src width height class srcset data-file-width data-file-height
//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/DiplomeMa%C3%A7onnique1945.png/220px-DiplomeMa%C3%A7onnique1945.png 220 156 thumbimage //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/DiplomeMa%C3%A7onnique1945.png/330px-DiplomeMa%C3%A7onnique1945.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/DiplomeMa%C3%A7onnique1945.png/440px-DiplomeMa%C3%A7onnique1945.png 2x 1824 1290
html
local
a
href class
/wiki/File:DiplomeMa%C3%A7onnique1945.png image
html
local
a
href class title
/wiki/File:DiplomeMa%C3%A7onnique1945.png internal Enlarge
html
local
div
class
magnify
html
local
a
href title
/wiki/Grande_Loge_de_France Grande Loge de France
html
local
i
html
local
div
class
thumbcaption
html
local
div
class style
thumb tleft thumbinner width:222px;
html
local
b
html
local
a
href title
/wiki/Shorthand Shorthand
html
local
a
href title
/wiki/Unicode Unicode
html
local
p
html
local
i
html
local
a
href title
/wiki/Asterism_(typography) Asterism (typography)
html
local
p
html
local
a
href title
/wiki/Station_model Station model
html
local
p
html
local
a
href class title
/wiki/Logical_implication mw-redirect Logical implication
html
local
a
href class title
/wiki/Entailment mw-redirect Entailment
html
local
a
href title
/wiki/Mathematical_logic Mathematical logic
html
local
a
href
#cite_note-3
html
local
sup
id class
cite_ref-3 reference
html
local
p
html
local
a
href class title
/wiki/Japanese_map_symbol mw-redirect Japanese map symbol
html
local
a
href class title
/wiki/Geographical_Survey_Institute_of_Japan mw-redirect Geographical Survey Institute of Japan
html
local
a
href title
/wiki/Ruins Ruins
html
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p
html
local
a
href title
/wiki/Tamil_script Tamil script
html
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a
href class title
/wiki/%C4%80ytam mw-redirect Āytam
html
local
a
href title
/wiki/Tamil_language Tamil language
html
local
p
html
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a
href class title
/wiki/Masonic mw-redirect Masonic
html
local
a
href title
/wiki/Abbreviation Abbreviation
html
local
a
href
#cite_note-Mackey-4
html
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sup
id class
cite_ref-Mackey_4-0 reference
html
local
p
html
local
a
href title
/wiki/Norwegian_language Norwegian language
html
local
a
href title
/wiki/Danish_language Danish language
html
local
i
html
local
a
href class title
/wiki/Open_o mw-redirect Open o
html
local
b
html
local
a
href
#cite_note-5
html
local
sup
id class
cite_ref-5 reference
html
local
p
html
local
span
class id
mw-headline See_also
html
local
span
class
mw-editsection-bracket
html
local
a
href title
/w/index.php?title=Therefore_sign&action=edit&section=4 Edit section: See also
html
local
span
class
mw-editsection-bracket
html
local
span
class
mw-editsection
html
local
h2
html
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