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"=" and "＝" redirect here. For double hyphens, see Double hyphen.
For other uses, see Equals (disambiguation).
For technical reasons, ":=" redirects here. For the computer programming assignment operator, see Assignment (computer science). For the definition symbol, see List of mathematical symbols#Symbols based on equality sign.
A well-known equality featuring the equals sign

The equals sign or equality sign (=) is a mathematical symbol used to indicate equality. It was invented in 1557 by Robert Recorde. The equals sign is placed between two expressions that have the same value meaning they represent the same mathematical object, as in an equation. It is assigned to the Unicode and ASCII character 003D in hexadecimal, 0061 in decimal.

History

The etymology of the word "equal" is from the Latin word "aequalis" as meaning "uniform", "identical", or "equal", from aequus ("level", "even", or "just").

The first use of an equals sign, equivalent to 14x+15=71 in modern notation. From The Whetstone of Witte by Robert Recorde.
Recorde's introduction of "="

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 gemellus[1]):

… 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 lines, of one length (thus =), because no two things can be more equal.

According to Scotland's University of St Andrews History of Mathematics 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.

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 mathematical definition, but with different semantics: the expression following "=" is evaluated first and may refer to a previous value of X. For example, the assignment X = X + 2 increases the value of X 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 if x = 2 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 (it was only possible to compare an expression to zero, using the arithmetic IF statement) until FORTRAN IV was released in 1962, since when it has used the four characters ".EQ." 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.

Usage of several equals signs

In PHP, the triple equals sign (===) denotes identity,[3] meaning that not only do the two expressions evaluate to equal values, 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 value.

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 ===.[4]

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 for 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 === on Range values means "inclusion in the range".[5] Note that under these semantics, === is non-symmetric; e.g. 1844 === (1800..1899) is false, since it is interpreted to mean Integer#=== rather than Range#===.[6]

Other uses

The equals sign is also used in defining attribute–value pairs, in which an attribute is assigned a value.[citation needed]

Tone letter

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.[7][8] The Unicode character used for the tone letter (U+A78A)[9] is different from the mathematical symbol (U+003D).

Related symbols

Approximately equal

Symbols used to denote items that are approximately equal include the following:[10]

Not equal

The symbol used to denote inequation (when items are not equal) is a slashed equals sign "≠" (U+2260; 2260,Alt+X in Microsoft Windows). In LaTeX, this is done with the "\neq" command.

Most programming languages, limiting themselves to the 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 "" or U+2254 ""), or a congruence relation in modular arithmetic. The symbol "" can be used to express that an item corresponds to another.

Isomorphism

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

In logic

Equality of truth values, i.e. bi-implication or logical equivalence, may be denoted by various symbols including =, ~, and ⇔.

In names

A 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 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.[11]

The equals sign is sometimes used in Japanese as a separator between names.

Other related symbols

Additional symbols in Unicode related to the equals sign include:[10]

• (U+224C all equal to)
• (U+2254 colon equals)
• (U+2255 equals colon)
• (U+2256 ring in equal to)
• (U+2257 ring equal to)
• (U+2259 estimates)
• (U+225A equiangular to)
• (U+225B star equals)
• (U+225C delta equal to)
• (U+225E measured by)
• (U+225F questioned equal to).

Incorrect usage

The equals 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 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 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.[12]

Notes

1. ^ See also geminus and Gemini.
2. ^ "Robert Recorde". MacTutor History of Mathematics archive. Retrieved 19 October 2013.
3. ^ "Comparison Operators". PHP.net. Retrieved 19 October 2013.
4. ^ Doug Crockford. "JavaScript: The Good Parts". YouTube. Retrieved 19 October 2013.
5. ^ why the lucky stiff. "5.1 This One’s For the Disenfranchised". why's (poignant) Guide to Ruby. Retrieved 19 October 2013.
6. ^ Brett Rasmussen (30 July 2009). "Don't Call it Case Equality". Retrieved 19 October 2013.
7. ^ Peter G. Constable; Lorna A. Priest (31 July 2006). Proposal to Encode Additional Orthographic and Modifier Characters (PDF). Retrieved 19 October 2013.
8. ^ Hartell, Rhonda L., ed. (1993). The Alphabets of Africa. Dakar: UNESCO and SIL. Retrieved 19 October 2013.
9. ^ "Unicode Latin Extended-D code chart" (PDF). Unicode.org. Retrieved 19 October 2013.
10. ^ a b "Mathematical Operators" (PDF). Unicode.org. Retrieved 19 October 2013.
11. ^ Gray, Carroll F. (November 2006). "The 1906 Santos=Dumont No. 14bis". World War I Aeroplanes. No. 194: 4.
12. ^ Capraro, Robert M.; Capraro, Mary Margaret; Yetkiner, Ebrar Z.; Corlu, Sencer M.; Ozel, Serkan; Ye, Sun; Kim, Hae Gyu (2011). "An International Perspective between Problem Types in Textbooks and Students' understanding of relational equality". Mediterranean Journal for Research in Mathematics Education 10 (1–2): 187–213. Retrieved 19 October 2013.

References

 196799 videos foundNext >
 The History of the Equals SignHow did the equal sign originate? We try to answer this question in 2 minutes or less, so learn more about it from this short history of the equality sign. IF you like ... Teaching the equals sign Equal means the sameThis is a very simple song that introduces students to the concept of "equal". In this song, students will hear the repetitive line, "Equal means the same" and the ... Equal, Greater or Less Thanhttp://www.mathsisfun.com/equal-less-greater.html As well as the familiar equals sign (=) it is also very useful to show if something is not equal to, greater than, ... Happy Equals SignAn Important Tip in Algebra is to Keep the Equals Sign Happy! ENTER is your Equals Sign TI 84 Calculator Introductionhttp://mcstutoring.com/ Private math tutoring and test preparation in Huntington Beach, CA. Subjects include ACT, SAT 1, algebra, geometry, and calculus. Comparing Decimals with Inequality and Equals Sign PHP Tutorial Video 6: More Variables, Numbers, and Plus Equals SignIn this PHP Tutorial, we'll look at numbers, and how to manipulate them with PHP. 1B CCSS 1 Understanding the Equals SignDr. Karlene Johnson, Greenville College, presents this topic as part of a series of lessons on the Common Core Standards for mathematics education. cuisenaire rods the way of zen 090 the equals signThe origin of the equals sign and its evolution towards "is equivalent to". This is for the benefit of young learners who will not fear mathematics. The music is one ...
 196799 videos foundNext >
 669 news items
 Huffington Post If We're Winning the Battle for Equality, Why Do People Keep Yelling "Faggot?" Huffington Post Wed, 26 Aug 2015 14:00:00 -0700 The team gets requests for their team T-shirt, an outline of the state of Alabama with an equals sign. People no longer have to whisper that they support the team. "I'm pleased with how supportive Montgomery has been," she says. Already this year her ... Rochester Democrat and Chronicle How to survive your freshman year in college Rochester Democrat and Chronicle Fri, 14 Aug 2015 08:55:33 -0700 When considering your next living situation, think “choice equals better” not “choice equals cool equals sign lease on building that should be condemned.” 4. Eat calories, don't drink them. You will consume additional calories. Despite the myths ... BGR 8 awesome iPhone and iPad apps on sale for free for a limited time BGR Tue, 04 Aug 2015 07:10:35 -0700 Instant Calculation calculates the formula as you type, so you never have to use the equals sign. We spare you one unnecessary tap at a time. ## You can start your calculations on your iPhone, then Continue on your Apple Watch, and the other way around. ABC Online Are calculators killing our ability to work it out in our head? ABC Online Sun, 09 Aug 2015 15:52:30 -0700 The child can explore the pattern made by entering 11+11 and continuing to press the equals sign to see what happens to the pattern once you count beyond 99 by 11s. Calculators have great potential in concept development. For example, what happens ... Review: Nyko PS4 Type Pad Hardcore Gamer Thu, 13 Aug 2015 08:00:00 -0700 A number of the keys, such as the equals sign and greater than, have also been assigned to the top most letters (below the numbers) and only require the Shift key to be pushed to access them. While these are usable design changes, the shift key is ... Hacklet 70 – Calculator Projects Hackaday Fri, 14 Aug 2015 16:00:43 -0700 No equals sign needed here; [Joey] designed this calculator to work with Reverse Polish notation, just like many of HP's early machines. Stacks are pretty important for RPN calculators, and this one has plenty of space with dual 200 layer stacks. The ... The Australian Financial Review Apps to help calm your everyday stress and anxieties The Australian Financial Review Thu, 30 Jul 2015 20:41:26 -0700 To cope with anxiety and stress, Opa would pour himself a cognac, sit in his room and complete complicated maths equations. Balancing the figures on each side of the equals sign was calming and a feeling of fresh satisfaction settled on his shoulders ... The Gay UK 1000 Anti-Gay Marriage Billboards To Be Erected In The USA The Gay UK Mon, 03 Aug 2015 01:48:42 -0700 The 14 foot by 48 foot billboard, shows icons of 1 man and one woman with the word "Marriage" and the equals sign. Underneath the tagline reads, "Please, I need your help with this! -God." The Church said,. "This billboard is funded 100% by the your ...
 Limit to books that you can completely read online Include partial books (book previews) .gsc-branding { display:block; }

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