The equality sign, equals sign, or "=" is a mathematical symbol used to indicate equality. It was invented in 1557 by Robert Recorde. The equals sign is placed between the things stated to have the same value, as in an equation. It is the Unicode and ASCII character 003D (in hexadecimal).
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The etymology of the word equal is from the Latin word aequalis, meaning "uniform, identical, or equal," from aequus "level, even, just."
The "=" symbol that is now universally accepted by mathematics for equality was first recorded by Welsh mathematician Robert Recorde in The Whetstone of Witte (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 gemini):
...to auoide the tediouſe repetition of theſe woordes : is equalle to : I will ſette as I doe often in woorke vſe, a paire of paralleles, or Gemowe lines of one lengthe, thus: =, bicauſe noe .2. thynges, can be moare equalle.
...to avoid the tedious repetition of these words: "is equal to", I will set (as I do often in work use) a pair of parallels (or Gemowe[1] lines) of one length (thus =), because no two things can be more equal.
According to Scotland's St Andrews University Maths History website:[2]
The symbol '=' was not immediately popular. The symbol || was used by some and æ (or œ), from the Latin word aequalis meaning equal, was widely used into the 1700s.
In mathematics, the equals sign is used for definitions (ex: let x = 2) as well as conditions and denoted equalities (ex: if x = 2 then x/2 = 1).
The 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.[3][4] The Unicode character used for the tone letter (U+A78A)[5] is different from the mathematical symbol (U+003D).
Traditional computer programming languages and their descendants (e.g. the Algol family, Pascal family, ADA, Eiffel, etc) use the equals sign as a boolean equality-operator as well as for defining constants, types, and parameters. This is consistent with mathematical usage and marks an intention for such languages to be as similar as possible to mathematical notation. A colon-equals (:=) is typically used to denote assignment.
In C-like languages, it is instead used as an assignment operator. C-like languages therefore use a double equals sign (==) as an equality operator.
Some languages (e.g. BASIC) use a single equals sign to denote both functions, sometimes with an optional let keyword to resolve any ambiguities.
In PHP, the triple equals sign (===) denotes identicalness,[6] meaning that not only do the two values evaluate to the same boolean value, they are also of the same data type. For instance, the expression 0 == false is true, but 0 === false is not, because the number 0 is an integer value (whereas false is a boolean).
JavaScript 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 0 == false is true, but 0 == undefined is false, even though both sides of the == act the same in boolean context. For this reason it is recommended to avoid the == operator in JavaScript in favor of ===.[7]
In Ruby, equality under == requires both operands to be of identical type, e.g. 0 == false is false. The === operator is flexible and may be defined arbitrarily by any given type. For example a value of type Range is a range of integers, such as 1800..1899. (1800..1899) == 1844 is false, since the types are different (Range vs. Integer); however (1800..1899) === 1844 is true, since Range defines === to mean "inclusion in the range".[8] Note that under these semantics, === is non-commutative; e.g. 1844 === (1800..1899) is false, since it is interpreted to mean Integer#=== rather than Range#===.[9]
Symbols used to denote items that are approximately equal are "wavy" equals signs.
The symbol used to denote inequation — when items are not equal — is a slashed equals sign "≠" (Unicode 2260).
Most programming languages, limiting themselves to the ASCII character set, use ~=, !=, /=, =/=, or <> to represent their boolean inequality operator.
The triple bar symbol "≡" (U+2261) is often used to indicate an identity, a definition (which can also be represented by "≝", U+225D), or a congruence relation in modular arithmetic. The symbol "≘" can be used to express that an item corresponds to another.
The symbol "≅" is often used to indicate isomorphic algebraic structures or congruent geometric figures. It can also mean very, very equal to.
Equality of truth values, i.e. bi-implication or logical equivalence, may be denoted by various symbols including =, ~, and ⇔.
A possibly unique case of the equal sign in a person's name, specifically in a double-barreled name, was by pioneer aviator Alberto Santos=Dumont, as he is also known to not only have often used 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.[10]
The equals sign can be used incorrectly within a mathematical argument, if used in a manner that connects steps of math in a non-standard way, rather than to show equality. For example, if one were finding the sum of the numbers 1, 2, 3, 4, and 5, one might say: 1 + 2 = 3 + 3 = 6 + 4 = 10 + 5 = 15. This is clearly incorrect, because each part of the equality has a different value. If interpreted strictly as it says, it implies 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[11].
