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The equals sign (
British English British English (BrE, en-GB, or BE) is, according to Oxford Dictionaries, "English as used in Great Britain, as distinct from that used elsewhere". More narrowly, it can refer specifically to the English language in England, or, more broadl ...
,
Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...
) or equal sign (
American English American English, sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. English is the most widely spoken language in the United States and in most circumstances ...
), also known as the equality sign, is the
mathematical symbol A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formul ...
, which is used to indicate equality in some well-defined sense. In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value. In
Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...
and
ASCII ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because ...
, it has the code point U+003D. It was invented in 1557 by Robert Recorde.


History

The etymology of the word "equal" is from the Latin word "''æqualis",'' as meaning "uniform", "identical", or "equal", from ''aequus'' ("level", "even", or "just"). The symbol, now universally accepted in mathematics for equality, was first recorded by Welsh mathematician Robert Recorde in ''
The Whetstone of Witte ''The Whetstone of Witte'' is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being ''The whetstone of , is the : The ''Coßike'' practise, with the rule of ''Equation'': and the of ''Surde Nombers. ...
'' (1557). The original form of the symbol was much wider than the present form. In his book Recorde explains his design of the "Gemowe lines" (meaning ''twin'' lines, from the
Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
'' gemellus'')See also geminus and Gemini. "The symbol was not immediately popular. The symbol was used by some and (or ), from the Latin word meaning equal, was widely used into the 1700s" (''History of Mathematics'', University of St Andrews).


Usage in mathematics and computer programming

In mathematics, the equal sign can be used as a simple statement of fact in a specific case (), or to create definitions (), conditional statements (), or to express a universal equivalence (). The first important computer programming language to use the equal sign was the original version of Fortran, FORTRAN I, designed in 1954 and implemented in 1957. In Fortran, serves as an assignment operator: sets the value of to 2. This somewhat resembles the use of in a mathematical definition, but with different semantics: the expression following is evaluated first, and may refer to a previous value of . For example, the assignment increases the value of by 2. A rival programming-language usage was pioneered by the original version of ALGOL, which was designed in 1958 and implemented in 1960. ALGOL included a relational operator that tested for equality, allowing constructions like with essentially the same meaning of as the conditional usage in mathematics. The equal sign was reserved for this usage. Both usages have remained common in different programming languages into the early 21st century. As well as Fortran, is used for assignment in such languages as C,
Perl Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages. "Perl" refers to Perl 5, but from 2000 to 2019 it also referred to its redesigned "sister language", Perl 6, before the latter's name was offic ...
, Python, awk, and their descendants. But is used for equality and not assignment in the
Pascal Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, Frenc ...
family,
Ada Ada may refer to: Places Africa * Ada Foah, a town in Ghana * Ada (Ghana parliament constituency) * Ada, Osun, a town in Nigeria Asia * Ada, Urmia, a village in West Azerbaijan Province, Iran * Ada, Karaman, a village in Karaman Province, T ...
, Eiffel, APL, and other languages. A few languages, such as BASIC and PL/I, have used the equal sign to mean both assignment and equality, distinguished by context. However, in most languages where has one of these meanings, a different character or, more often, a sequence of characters is used for the other meaning. Following ALGOL, most languages that use for equality use for assignment, although APL, with its special character set, uses a left-pointing arrow. Fortran did not have an equality operator (it was only possible to compare an expression to zero, using the arithmetic IF statement) until FORTRANIV was released in 1962, since when it has used the four characters to test for equality. The language B introduced the use of with this meaning, which has been copied by its descendant C and most later languages where means assignment. The equal sign is also used in defining attribute–value pairs, in which an attribute is assigned a
value Value or values may refer to: Ethics and social * Value (ethics) wherein said concept may be construed as treating actions themselves as abstract objects, associating value to them ** Values (Western philosophy) expands the notion of value beyo ...
.


Several equal signs

In PHP, the triple equal sign, , denotes value and type equality, meaning that not only do the two expressions evaluate to equal values, but they are also of the same data type. For instance, the expression is true, but is not, because the number 0 is an integer value whereas false is a Boolean value.
JavaScript JavaScript (), often abbreviated as JS, is a programming language that is one of the core technologies of the World Wide Web, alongside HTML and CSS. As of 2022, 98% of websites use JavaScript on the client side for webpage behavior, of ...
has the same semantics for , referred to as "equality without type coercion". However, in JavaScript the behavior of cannot be described by any simple consistent rules. The expression is true, but is false, even though both sides of the act the same in Boolean context. For this reason it is sometimes recommended to avoid the operator in JavaScript in favor of . In Ruby, equality under requires both operands to be of identical type, e.g. is false. The operator is flexible and may be defined arbitrarily for any given type. For example, a value of type is a range of integers, such as . is false, since the types are different (Range vs. Integer); however is true, since on values means "inclusion in the range". Under these semantics,

is non-symmetric; e.g. 1844 

 (1800..1899)
is false, since it is interpreted to mean Integer#

rather than Range#

. In most programming languages,

is used to check equality, so 1844 

1844
will return true.


Other uses


Spelling


Tone letter

The equal sign is also used as a grammatical tone letter in the orthographies of Budu in the Congo-Kinshasa, in Krumen, Mwan and
Dan Dan or DAN may refer to: People * Dan (name), including a list of people with the name ** Dan (king), several kings of Denmark * Dan people, an ethnic group located in West Africa **Dan language, a Mande language spoken primarily in Côte d'Ivoir ...
in the Ivory Coast. The Unicode character used for the tone letter (U+A78A) is different from the mathematical symbol (U+003D).


Personal names

A possibly unique case of the equal sign of European usage in a person's name, specifically in a
double-barreled name A double-barrelled name is a type of compound surname, typically featuring two words (occasionally more), often joined by a hyphen. Examples of some notable people with double-barrelled names include Winnie Madikizela-Mandela and Sacha Baron Co ...
, was by pioneer aviator
Alberto Santos-Dumont Alberto Santos-Dumont ( Palmira, 20 July 1873 — Guarujá, 23 July 1932) was a Brazilian aeronaut, sportsman, inventor, and one of the few people to have contributed significantly to the early development of both lighter-than-air and heavie ...
, as he is also known not only to have often used a
double hyphen In Latin script, the double hyphen is a punctuation mark that consists of two parallel hyphens. It was a development of the earlier , which developed from a Central European variant of the virgule slash, originally a form of scratch comma. S ...
resembling an equal sign between his two surnames in place of a hyphen, but also seems to have personally preferred that practice, to display equal respect for his father's French ethnicity and the Brazilian ethnicity of his mother. Instead of a double hyphen, the equal sign is sometimes used in Japanese as a separator between names. In Ojibwe, the readily available equal sign on a keyboard is used as a substitute for a double hyphen.


Linguistics

In linguistic interlinear glosses, an equal sign is conventionally used to mark clitic boundaries: the equal sign is placed between the clitic and the word that the clitic is attached to.


Chemistry

In
chemical formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
s, the two parallel lines denoting a double bond are commonly rendered using an equal sign.


LGBT symbol

In recent years, the equal sign has been used to symbolize
LGBT rights Rights affecting lesbian, gay, bisexual, and transgender ( LGBT) people vary greatly by country or jurisdiction—encompassing everything from the legal recognition of same-sex marriage to the death penalty for homosexuality. Notably, ...
. The symbol has been used since 1995 by the Human Rights Campaign, which lobbies for marriage equality, and subsequently by the United Nations Free & Equal, which promotes LGBT rights at the United Nations.


Hate speech

The not equal (≠) symbol has been adopted by some white supremacist and other racist groups.


Telegrams and Telex

In Morse code, the equal sign is encoded by the letters B (-...) and T (-) run together (-...-). The letters BT stand for Break Text, and are put between paragraphs, or groups of paragraphs in messages sent via Telex, a standardised tele-typewriter. The sign, used to mean Break Text, is given at the end of a telegram to separate the text of the message from the signature.


Related symbols


Approximately equal

Symbols used to denote items that are '' approximately equal'' include the following: * (, LaTeX ''\approx'') * (, LaTeX ''\simeq''), a combination of and , also used to indicate asymptotic equality * (, LaTeX ''\cong''), another combination of ≈ and =, which is also sometimes used to indicate isomorphism or congruence * (, LaTeX ''\sim''), which is also sometimes used to indicate proportionality or similarity, being related by an equivalence relation, or to indicate that a random variable is distributed according to a specific probability distribution (see also tilde) * (, LaTex ''\backsim''), which is also used to indicate proportionality * (, LaTeX ''\doteq''), which can also be used to represent the approach of a variable to a
limit Limit or Limits may refer to: Arts and media * ''Limit'' (manga), a manga by Keiko Suenobu * ''Limit'' (film), a South Korean film * Limit (music), a way to characterize harmony * "Limit" (song), a 2016 single by Luna Sea * "Limits", a 2019 ...
* (, LaTeX ''\fallingdotseq''), commonly used in Japan, Taiwan, and Korea. * (, LaTex ''\risingdotseq'') In some areas of East Asia such as Japan, "≒" is used to mean "the two terms are almost equal", but in other areas and specialized literature such as mathematics, "≃" is often used. In addition to its mathematical meaning, it is sometimes used in Japanese sentences with the intention of "almost the same."


Not equal

The symbol used to denote
inequation In mathematics, an inequation is a statement that an inequality holds between two values. It is usually written in the form of a pair of expressions denoting the values in question, with a relational sign between them indicating the specific in ...
(when items are not equal) is a slashed equal sign (U+2260). In LaTeX, this is done with the "\neq" command. Most programming languages, limiting themselves to the 7-bit ASCII character set and typeable characters, use , , , or to represent their Boolean inequality operator.


Identity

The triple bar symbol (U+2261, LaTeX ''\equiv'') is often used to indicate an
identity Identity may refer to: * Identity document * Identity (philosophy) * Identity (social science) * Identity (mathematics) Arts and entertainment Film and television * ''Identity'' (1987 film), an Iranian film * ''Identity'' (2003 film), an ...
, a definition (which can also be represented by or ), or a congruence relation in modular arithmetic.


Isomorphism

The symbol is often used to indicate isomorphic algebraic structures or congruent geometric figures.


In logic

Equality of truth values (through bi-implication or logical equivalence), may be denoted by various symbols including , , and .


Other related symbols

Additional precomposed symbols with code points in Unicode for notations related to the equal sign include: * () * () (see also
assignment (computer science) In computer programming, an assignment statement sets and/or re-sets the value stored in the storage location(s) denoted by a variable name; in other words, it copies a value into the variable. In most imperative programming languages, the as ...
for ) * () * () * () * () * () * () * () * () * () * () * () (see also Backus–Naur form for ) * () * ()


Incorrect usage

The equal sign is sometimes used incorrectly within a mathematical argument to connect math steps in a non-standard way, rather than to show equality (especially by early mathematics students). For example, if one were finding the sum, step by step, of the numbers 1, 2, 3, 4, and 5, one might incorrectly write :1 + 2 = 3 + 3 = 6 + 4 = 10 + 5 = 15. Structurally, this is shorthand for :( 1 + 2 = 3) + 3 = 6+ 4 = 10) + 5 = 15, but the notation is incorrect, because each part of the equality has a different value. If interpreted strictly as it says, it would imply that :3 = 6 = 10 = 15 = 15. A correct version of the argument would be :1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, 10 + 5 = 15. This difficulty results from subtly different uses of the sign in education. In early, arithmetic-focused grades, the equal sign may be ''operational''; like the equal button on an electronic calculator, it demands the result of a calculation. Starting in algebra courses, the sign takes on a ''relational'' meaning of equality between two calculations. Confusion between the two uses of the sign sometimes persists at the university level.


Encodings

* Related: *


See also

* 2 + 2 = 5 *
Double hyphen In Latin script, the double hyphen is a punctuation mark that consists of two parallel hyphens. It was a development of the earlier , which developed from a Central European variant of the virgule slash, originally a form of scratch comma. S ...
* Equality (mathematics) * Logical equality * Plus and minus signs


Notes


References

* * Boyer, C. B.: ''A History of Mathematics'', 2nd ed. rev. by Uta C. Merzbach. New York: Wiley, 1989 (1991 pbk ed. )


External links


Earliest Uses of Symbols of RelationImage of the page of ''The Whetstone of Witte'' on which the equal sign is introduced
{{DEFAULTSORT:Equal Sign Mathematical symbols Welsh inventions 1557 introductions Definition Assignment operations Equivalence (mathematics)