词条 | Equals sign |
释义 |
HistoryThe 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 that is now universally accepted in 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]):[2] 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.
According to Scotland's University of St Andrews History of Mathematics website:[3] 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 programmingIn 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 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: 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 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. The equals sign is also used in defining attribute–value pairs, in which an attribute is assigned a value.{{ctn|date=June 2013}} Usage of several equals signsIn PHP, the triple equals sign ( === , 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 sometimes recommended to avoid the == operator in JavaScript in favor of === .[5]In Ruby, equality under Other usesThe equals sign is sometimes used in Japanese as a separator between names. SpellingTone 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.[8][9] The Unicode character used for the tone letter (U+A78A)[10] is different from the mathematical symbol (U+003D). 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 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] 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.[12] ChemistryIn chemical formulas, the two parallel lines denoting a double bond are commonly rendered using an equals sign. LGBT symbol{{Expand section|date=July 2018}}In 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.[13] Related symbols{{See also|Unicode mathematical operators}}Approximately equal{{Main|Approximation#Unicode}}Symbols used to denote items that are approximately equal include the following:[14]
Not equalThe 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 "\eq" command. Most programming languages, limiting themselves to the 7-bit ASCII character set and typeable characters, use IdentityThe 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. 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:[14]
Incorrect usageThe 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 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 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. 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.[15] Encodings
Related:
See also
Notes1. ^See also geminus and Gemini. 2. ^Recorde, Robert, The Whetstone of Witte … (London, England: Jhon Kyngstone, 1557), [https://archive.org/stream/TheWhetstoneOfWitte#page/n237/mode/2up the third page of the chapter "The rule of equation, commonly called Algebers Rule."] 3. ^{{cite web | url = http://www-history.mcs.st-and.ac.uk/Mathematicians/Recorde.html | website = MacTutor History of Mathematics archive | title = Robert Recorde | accessdate = 19 October 2013}} 4. ^{{cite web| url = http://www.php.net/manual/en/language.operators.comparison.php| title = Comparison Operators| website = PHP.net| accessdate = 19 October 2013}} 5. ^{{cite web| last = Crockford| first = Doug| title = JavaScript: The Good Parts| website = YouTube| url = https://www.youtube.com/watch?v=hQVTIJBZook| accessdate = 19 October 2013}} 6. ^{{cite book| title = why's (poignant) Guide to Ruby| chapter = 5.1 This One’s For the Disenfranchised| author = why the lucky stiff| chapter-url = http://mislav.uniqpath.com/poignant-guide/book/chapter-5.html#section1| accessdate = 19 October 2013}} 7. ^{{cite web| last = Rasmussen| first = Brett| title = Don't Call it Case Equality| date = 30 July 2009| url = http://www.pmamediagroup.com/2009/07/dont-call-it-case-equality/| website = pmamediagroup.com| accessdate = 19 October 2013}} 8. ^{{cite book | author = Peter G. Constable | author2 = Lorna A. Priest | url = https://www.unicode.org/L2/L2006/06259r-mod-letters.pdf | title = Proposal to Encode Additional Orthographic and Modifier Characters | date = 31 July 2006 | accessdate = 19 October 2013}} 9. ^{{cite book | editor = Hartell, Rhonda L. | year = 1993 | title = The Alphabets of Africa | location = Dakar | publisher = UNESCO and SIL | url = https://archive.org/details/rosettaproject_pbi_ortho-1 | accessdate = 19 October 2013}} 10. ^{{cite web | title = Unicode Latin Extended-D code chart | website = Unicode.org | url = https://www.unicode.org/charts/PDF/UA720.pdf | accessdate = 19 October 2013}} 11. ^{{cite journal |last=Gray |first=Carroll F.|title=The 1906 Santos=Dumont No. 14bis |journal=World War I Aeroplanes |volume=No. 194 |date=November 2006 |page=4}} 12. ^{{Cite web|title = Conventions for interlinear morpheme-by-morpheme glosses| url = https://www.eva.mpg.de/lingua/resources/glossing-rules.php| access-date = 2017-11-20 }} 13. ^"HRC Story: Our Logo." The Human Rights Campaign. HRC.org, Retrieved 4 December 2018. 14. ^1 {{cite web | title = Mathematical Operators | website = Unicode.org | url = https://www.unicode.org/charts/PDF/U2200.pdf | accessdate = 19 October 2013}} 15. ^{{cite journal | url = https://tamu.academia.edu/SencerCorlu/Papers/522225/Capraro_R._M._Capraro_M._M._Yetkiner_Z._E._Corlu_M._S._Ozel_S._Ye_S._and_Kim_H._G._2011_._An_international_perspective_between_problem_types_in_textbooks_and_students_understanding_of_relational_equality._Mediterranean_Journal_for_Research_in_Mathematics_Education_An_International_Journal_10_187-213 | title = An International Perspective between Problem Types in Textbooks and Students' understanding of relational equality | last = Capraro | first = Robert M. | last2 = Capraro | first2 = Mary Margaret | last3 = Yetkiner | first3 = Ebrar Z. | last4 = Corlu | first4 = Sencer M. | last5 = Ozel | first5 = Serkan | last6 = Ye | first6 = Sun | last7 = Kim | first7 = Hae Gyu | journal = Mediterranean Journal for Research in Mathematics Education | volume = 10 | number = 1–2 | pages = 187–213 | year = 2011 | accessdate = 19 October 2013}} References
External links
6 : Mathematical symbols|Welsh inventions|1557 introductions|Definition|Assignment operations|Equivalence (mathematics) |
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