# 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
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 &#61;or in HTML &#x3D;.

## 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 ).

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+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 ${\ displaystyle: =}$ 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.