The equals sign or equality sign, =, is a mathematical symbol used to indicate equality in some well-defined sense.[1][2] 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.
History
The etymology of the word "equal" is from the Latin word "æqualis",[3] 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 (1557).[4] 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 gemellus[5]
And 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.[6]
"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" (History of Mathematics, University of St Andrews).[7]
Usage in mathematics and computer programming
In mathematics, the equals sign can be used as a simple statement of fact in a specific case (x = 2), or to create definitions (let x = 2), conditional statements (if x = 2, then ...), or to express a universal equivalence ((x + 1)² = x² + 2x + 1).
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: X = 2 sets the value of X to 2. This somewhat resembles the use of = in a math
The etymology of the word "equal" is from the Latin word "æqualis",[3] 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 (1557).[4] 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 gemellus[5]
And 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.[6]
"The symbol = was not immediately popular. The symbol || was used by some and æ (or œ), from the Latin word aequalis meaning equal, w
The = symbol, now universally accepted in mathematics for equality, was first recorded by Welsh mathematician Robert Recorde in The Whetstone of Witte (1557).[4] 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 gemellus[5]
And 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.[6]
"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" (
"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" (History of Mathematics, University of St Andrews).[7]
Usage in mathematics and computer programming
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.[15]
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.
Linguistics
In 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.[16]
Chemistry
In
In 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.[17]
Use in Telegrams and Telex
In Morse code, the equals sign is encoded by the letters B (-...) and T (-) run together (-...-).[citation needed] The letters BT stand for Break Text, and are put between paragraphs, or groups of paragraphs in messages sent via Telex,[citation needed] a standardised tele-typewriter. The sign, used to mean Break Text, is given at the end of a Morse code, the equals sign is encoded by the letters B (-...) and T (-) run together (-...-).[citation needed] The letters BT stand for Break Text, and are put between paragraphs, or groups of paragraphs in messages sent via Telex,[citation needed] 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.[18][better source needed]
Related symbols
approximately equal include the following:[1][19]
- ≈ (U+2248, LaTeX \approx)
- ≃ (U+2243, LaTeX \simeq), a combination of ≈ and =, also used to indicate asymptotic equality
- ≅ (U+2245, LaTeX \cong), another combination of ≈ and =, which is also sometimes used to indicate isomorphism or congruence
- ∼ (U+223C, LaTeX \sim), which is also sometimes used to indicate proportionality or sim
The symbol used to denote inequation (when items are not equal) is a slashed equals 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, a definition (which can also be represented by U+225D ≝ EQUAL TO BY DEFINITION or U+2254 ≔ COLON EQUALS), or a congruence relation in modular arithmetic.[1]
7-bit ASCII
character set and typeable characters, use ~=, !=, /=, or <> to represent their Boolean inequality operator.
The triple bar symbol ≡ (U+2261, LaTeX \equiv) is often used to indicate an identity, a definition (which can also be represented by U+225D ≝ EQUAL TO BY DEFINITION or U+2254 ≔ COLON EQUALS), or a congruence relation in modular arithmetic.[1]
IsomorphismThe symbol ≅ is often used to indicate isomorphic algebraic structures or congruent geometric figures.[1]
In logic
Equali
Equality of truth values (through bi-implication or logical equivalence), may be denoted by various symbols including =, ~, and ⇔.
- U+003D = EQUALS SIGN (HTML
= · =)
Related:
- U+2260 ≠ NOT EQUAL TO (HTML
≠ · ≠, ≠)
See also
Notes
- ^ a b c d "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-09.
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.
Linguistics
In 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.[16]
Chemistry
In
In 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.[17]
Use in Telegrams and Telex
In Morse code, the equals sign is encoded by the letters B (-...) and T (-) run together (-...-).[citation needed] The letters BT stand for Break Text, and are put between paragraphs, or groups of paragraphs in messages sent via Telex,[citation needed] a standardised tele-typewriter. The sign, used to mean Break Text, is given at the end of a Morse code, the equals sign is encoded by the letters B (-...) and T (-) run together (-...-).[citation needed] The letters BT stand for Break Text, and are put between paragraphs, or groups of paragraphs in messages sent via Telex,[citation needed] 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.[18][better source needed]
Related symbols
approximately equal include the following:[1][19]
- ≈ (U+2248, LaTeX \approx)
- ≃ (U+2243, LaTeX \simeq), a combination of ≈ and =, also used to indicate asymptotic equality
- ≅ (U+2245, LaTeX \cong), another combination of ≈ and =, which is also sometimes used to indicate isomorphism or congruence
- ∼ (U+223C, LaTeX \sim), which is also sometimes used to indicate proportionality or sim
The symbol used to denote inequation (when items are not equal) is a slashed equals 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, a definition (which can also be represented by U+225D ≝ EQUAL TO BY DEFINITION or U+2254 ≔ COLON EQUALS), or a congruence relation in modular arithmetic.[1]
7-bit ASCII
character set and typeable characters, use ~=, !=, /=, or <> to represent their Boolean inequality operator.
The triple bar symbol ≡ (U+2261, LaTeX \equiv) is often used to indicate an identity, a definition (which can also be represented by U+225D ≝ EQUAL TO BY DEFINITION or U+2254 ≔ COLON EQUALS), or a congruence relation in modular arithmetic.[1]
IsomorphismThe symbol ≅ is often used to indicate isomorphic algebraic structures or congruent geometric figures.[1]
In logic
Equali
Equality of truth values (through bi-implication or logical equivalence), may be denoted by various symbols including =, ~, and ⇔.
- U+003D = EQUALS SIGN (HTML
= · =)
Related:
- U+2260 ≠ NOT EQUAL TO (HTML
≠ · ≠, ≠)
See also
Notes
- ^ a b c d "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-09.
- ≈ (U+2248, LaTeX \approx)
- ≃ (U+2243, LaTeX \simeq), a combination of ≈ and =, also used to indicate asymptotic equality
- ≅ (U+2245, LaTeX \cong), another combination of ≈ and =, which is also sometimes used to indicate isomorphism or congruence
- ∼ (U+223C, LaTeX \sim), which is also sometimes used to indicate proportionality or sim
The symbol used to denote inequation (when items are not equal) is a slashed equals 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, a definition (which can also be represented by U+225D ≝ EQUAL TO BY DEFINITION or U+2254 ≔ COLON EQUALS), or a congruence relation in modular arithmetic.[1]
7-bit ASCII
character set and typeable characters, use~=,!=,/=, or<>to represent their Boolean inequality operator.The triple bar symbol ≡ (U+2261, LaTeX \equiv) is often used to indicate an identity, a definition (which can also be represented by U+225D ≝ EQUAL TO BY DEFINITION or U+2254 ≔ COLON EQUALS), or a congruence relation in modular arithmetic.[1]
IsomorphismThe symbol ≅ is often used to indicate isomorphic algebraic structures or congruent geometric figures.[1]
In logic
Equali
Equality of truth values (through bi-implication or logical equivalence), may be denoted by various symbols including =, ~, and ⇔.
- U+003D = EQUALS SIGN (HTML
=·=)
Related:
- U+2260 ≠ NOT EQUAL TO (HTML
≠·≠, ≠)
See also
Notes
- ^ a b c d "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-09.
- U+003D = EQUALS SIGN (HTML