The equals sign or equality sign, , is a mathematical symbol used to indicate equality. It was invented in 1557 by Robert Recorde. In an equation, the equals sign 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 and ASCII, it has the code point, 3D.
HistoryThe etymology of the word "equal" is from the Latin word "æqualis" as meaning "uniform", "identical", or "equal", from aequus.
by Robert Recorde.
The symbol, now universally accepted in mathematics for equality, was first recorded by Welsh mathematician Robert Recorde in The Whetstone of Witte''. The original form of the symbol was much wider than the present form. In his book Recorde explains his design of the "Gemowe lines", from the Latin word aequalis meaning equal, was widely used into the 1700s".
Usage in mathematics and computer programmingIn mathematics, the equals 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 equals 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 equals 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, Python, awk, and their descendants. But is used for equality and not assignment in the Pascal family, Ada, Eiffel, APL, and other languages.
A few languages, such as BASIC and PL/I, have used the equals 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 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 equals sign is also used in defining attribute–value pairs, in which an attribute is assigned a value.
Usage of several equals signsIn PHP, the triple equals 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.
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 ; however is true, since on values means "inclusion in the range". Under these semantics,
is non-symmetric; e.g.
1844is false, since it is interpreted to mean
Tone letterThe equals sign is also used as a grammatical tone letter in the orthographies of Budu in the Congo-Kinshasa, in Krumen, Mwan and Dan in the Ivory Coast. The Unicode character used for the tone letter is different from the mathematical symbol.
Personal namesA possibly unique case of the equals sign of European usage in a person's name, specifically in a double-barreled name, was by pioneer aviator Alberto Santos-Dumont, as he is also known not only to have often used a double hyphen resembling an equals 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 equals 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.
LinguisticsIn linguistic interlinear glosses, an equals sign is conventionally used to mark clitic boundaries: the equals sign is placed between the clitic and the word that the clitic is attached to.
ChemistryIn chemical formulas, the two parallel lines denoting a double bond are commonly rendered using an equals sign.
LGBT symbolIn recent years, the equals sign has been used to symbolize LGBT rights. 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.
Approximately equalSymbols used to denote items that are approximately equal include the following:
- ≃, a combination of ≈ and =, also used to indicate asymptotic equality
- ≅, another combination of ≈ and =, which is also sometimes used to indicate isomorphism or congruence
- ∼, 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
- ∽, which is also used to indicate proportionality
- ≐, which can also be used to represent the approach of a variable to a limit
- ≒, commonly used in Japan, Taiwan and Korea.
Most programming languages, limiting themselves to the 7-bit ASCII character set and typeable characters, use,,, or to represent their Boolean inequality operator.
IdentityThe triple bar symbol is often used to indicate an identity, a definition, or a congruence relation in modular arithmetic.
IsomorphismThe symbol is often used to indicate isomorphic algebraic structures or congruent geometric figures.
In logicEquality of truth values, i.e. bi-implication or logical equivalence, may be denoted by various symbols including,, and.
Other related symbolsAdditional symbols in Unicode related to the equals sign include:
For example, if one were finding the sum, step by step, of the numbers 1, 2, 3, 4, and 5, one might incorrectly write
Structurally, this is shorthand for
but the notation is incorrect, because each part of the equality has a different value. If interpreted strictly as it says, it implies
A correct version of the argument would be
This difficulty results from subtly different uses of the sign in education. In early, arithmetic-focused grades, the equals sign may be operational; like the equals 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.