Equal sign

=
Mathematical signs
arithmetic
Plus sign	+
Minus sign	- , ./.
Mark	⋅ , ×
Divided sign	: , ÷ , /
Plus minus sign	± , ∓
Comparison sign	< , ≤ , = , ≥ , >
Root sign	√
Percent sign	%
Analysis
Sum symbol	Σ
Product mark	Π
Difference sign , Nabla	∆ , ∇
Prime	′
Partial differential	∂
Integral sign	∫
Concatenation characters	∘
Infinity symbol	∞
geometry
Angle sign	∠ , ∡ , ∢ , ∟
Vertical , parallel	⊥ , ∥
Triangle , square	△ , □
Diameter sign	⌀
Set theory
Union , cut	∪ , ∩
Difference , complement	∖ , ∁
Element character	∈
Subset , superset	⊂ , ⊆ , ⊇ , ⊃
Empty set	∅
logic
Follow arrow	⇒ , ⇔ , ⇐
Universal quantifier	∀
Existential quantifier	∃
Conjunction , disjunction	∧ , ∨
Negation sign	¬

In mathematics , formal logic and in the exact natural sciences , the equal sign ( = , also called is-equal sign ) stands between two expressions with the same value .

history

Introduction of the equal sign 1557, followed by “14x + 15 = 71” as the first printed equation

In ancient and medieval mathematics, the equality of two expressions was still literally written down (e.g. est egale for "is equal"). Descartes (1596–1650) shortened this with a æ (for Latin aequalis ) rotated by 180 ° , with the horizontal line being more and more omitted in the subsequent period. This symbol survived in the form ∝ as one of the proportionality symbols . As the founder of modern equal sign the Welsh mathematician applies Robert Recorde (1510-1558) with his book The Whetstone of Witte , dt (1557). The whetstone of knowledge . He justified the two parallel lines for an equality symbol with the early New English sentence … bicause noe.2.thynges, can be moare equalle. (Today's English: because no two things can be more equal , " because no two things can be the same").

The =, which was already used in England , was probably first introduced on the European continent by Gottfried Wilhelm Leibniz (1646–1716).

presentation

The equal sign is coded in ASCII with 61 ( decimal ), so as Unicode U + 003D (61 decimal = 3D hexadecimal ). It is not one of the named entities in markup languages , but can be replaced with =or in HTML =.

use

General use

The glyph = is generally used to represent facts of correspondence, equality or identity , in mathematics, computer science and technology also the assignment in the sense of a subsequent equal use.

The equal sign is often used as a substitute for the double hyphen ⹀ (U + 2E40) or its Japanese variant (U + 30A0).

In electrical engineering , the equal sign is used to identify direct voltage .

The equal sign and its variations

There are also modified forms with a different meaning, such as B. the equivalent sign (≙) or the rounding sign ( ≈) with the meaning approximately equal / rounded . If the inequality of two numbers is to be shown, a crossed out equal sign (≠) is used. A shape with three horizontal bars (≡) is used to indicate the identity of two arithmetic expressions.

The modifications: = or =: are used in mathematics to represent a definition of one side by the other side. The colons are always next to the object to be defined. The ≡ previously used for this should no longer be used in this sense ( DIN 1302 ), but shapes such as (DIN 1302) or ( ISO 31 -11) are possible. ${\ displaystyle {=} _ {\ mathrm {def}}}$ ${\ displaystyle {} {\ stackrel {\ mathrm {def}} {=}}}$

For example, the set A can be defined as follows:

{\ displaystyle A \ {\ stackrel {\ mathrm {def}} {=}} \ \ {2; 4; 7; 9 \} \ \ mathrm {or} \ A: = \ {2; 4; 7; 9 \} \ \ mathrm {or} \ \ {2; 4; 7; 9 \} =: A.}

In programming languages that are derived from C , the (simple) equal sign is used for value assignment . In these languages, however, a double equal sign ( == ) is usually used as the comparison operator . In Fortran is used for the comparison operator. In languages of the Pascal family, on the other hand, a: = is used for the assignment (in the predecessor Algol 60 this character combination or also a "←") and the equal sign as a comparison operator. There are also languages such as B. BASIC , in which it is always clear from the context whether it is an assignment or a comparison and therefore use the equal sign for both the assignment and the comparison operator. .EQ.

Inequality sign

Since the character for inequality ≠ is not available in the ASCII character set, various programming languages use digraphs such as <>(Pascal, BASIC), /=(Ada), !=( not equal , C, C ++) or ~=(ML); Fortran used .NE.(because of English n ot e qual , not equal ).

Mathematical equivalence signs
Z.	Unicode	meaning	description	Z.	Unicode	meaning	description
=	`U+003D`	equal		≠	`U+2260`	unequal; not equal ⁽¹⁾
≡	`U+2261`	congruent , identical		≢	`U+2262`	not congruent ⁽¹⁾
≐	`U+2250`	Limit value approximation
≃	`U+2243`	asymptotically equal		≄	`U+2244`	asymptotically unequal ⁽¹⁾
≂	`U+2242`		Minus tildes
≅	`U+2245`	approximately equal (Anglo-American, according to DIN only permissible for asymptotically equal (≃))		≆	`U+2246`	roughly, but not exactly the same
≅	`U+2245`			≇	`U+2247`	neither roughly nor exactly the same
${\ displaystyle \ cong}$		isomorphic , isomorphic in terms of category theory
≊	`U+224A`	about the same or equal
≈	`U+2248`	roughly equal / rounded ( coll .: almost equal )	Double tilde	≉	`U+2249`	not about the same (coll .: not almost the same )	Crossed out double tildes
≋	`U+224B`		Triple tilde
≗	`U+2257`	about the same
≒	`U+2252`	roughly the same or picture		≓	`U+2253`	Picture or about the same
≌	`U+224C`	all the same
≍	`U+224D`	equivalent to
≣	`U+2263`	exactly equivalent
≎	`U+224E`	geometrically equivalent
≏	`U+224F`	Difference between
≑	`U+2251`	geometrically the same
≚	`U+225A`	equiangular
≔	`U+2254`	results from (for definition on the left (: =) not provided)		≕	`U+2255`	does not result from (for definition on the right (= :) not provided)
≜	`U+225C`	right by definition
≝	`U+225D`	right by definition
${\ displaystyle: =}$		Definition on the left	Colon + equal sign	${\ displaystyle =:}$		Right-hand definition	Equal sign + colon
${\ displaystyle {\ stackrel {!} {=}}}$		should be the same (for example in the introduction of evidence )
≙	`U+2259`	corresponds
≘	`U+2258`	corresponds to (unusual)
≞	`U+225E`	measured
≟	`U+225F`	maybe right away
≛	`U+225B`		Star is the same
≖	`U+2256`		Circle in equal sign

⁽¹⁾ DIN 1302prescribes vertical strikethrough, but allows oblique strikethrough "if it is necessary for reasons of composition technology". ISO 31generally allows both forms.

Individual evidence

↑ ... and written “is equal sign”; see also in the DWDS , under the equal sign , there also with "actual equal sign" (accessed on November 15, 2018)
^ Robert Recorde : The Whetstone of Witte . London 1557, p. 238.
↑ Matthias Helle: = . In: FU Berlin, Institute for Computer Science (Ed.): Seminar History of Mathematical Notation . 1999 (fu-berlin.de; script for the lecture on July 21, 1999).
↑ ^a ^b Hans Friedrich Ebel , Claus Bliefert , Walter Greulich : Writing and publishing in the natural sciences . Wiley-VCH, 2006, ISBN 978-3-527-30802-6 , 6.5.4 Frequently occurring special characters , p. 352 ff . ( limited preview in Google Book search).

[DWDS-1] ... and written “is equal sign”; see also in the DWDS , under the equal sign , there also with "actual equal sign" (accessed on November 15, 2018)

[2] Robert Recorde : The Whetstone of Witte . London 1557, p. 238.

[Helle-3] Matthias Helle: = . In: FU Berlin, Institute for Computer Science (Ed.): Seminar History of Mathematical Notation . 1999 (fu-berlin.de; script for the lecture on July 21, 1999).

[Ebel-4] Hans Friedrich Ebel , Claus Bliefert , Walter Greulich : Writing and publishing in the natural sciences . Wiley-VCH, 2006, ISBN 978-3-527-30802-6 , 6.5.4 Frequently occurring special characters , p. 352 ff . ( limited preview in Google Book search).