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The equal sign, equals sign, or "=" is a mathematical symbol used to indicate equality. It was invented in 1557 by Welshman Robert Recorde. The equals sign is placed between the things stated to be exactly the same, as in an equation. It is the Unicode and ASCII character 003D (in hexadecimal).
History
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 use, 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.
However, a manuscript from the University of Bologna, dated from 1550–68, features the same equality symbol, possibly predating its usage by Recorde.[citation needed] 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.
Related symbols
A symbol used to denote items that are approximately equal is "≈" (wave lines; Unicode character 2248), and the symbol used to denote when items are not equal is "≠" (slashed equal sign; Unicode character 2260).
The symbol "≡" (Unicode character 2261) is often used to indicate an identity, 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.
Equality of truth values, i.e. bi-implication or logical equivalence, may be denoted by various symbols including =, ~, and <=>.
In programming languages
Most programming languages, which are limited to the ASCII character set, use "~=", "!=", "/=", "=/=" or "<>" to represent "not equal to"; "!=" has carried over into newsgroups and Internet forums.
In programming languages, the equals sign may either denote a boolean operator to test equality of values (sometimes a double equal sign "=="), or it may denote an assignment (sometimes denoted with a colon-equals ":="). In some programming languages such as PHP a double equals sign ("==") denotes equivalence, meaning that the variables may not be of the same data type, but their values can be reduced to the same value. The triple equal sign ("===") denotes identity[1], meaning that not only do the two values parse to be the same, they are of the same data type. For instance, in PHP the expression ("0 == false") is true, but ("0 === false") is not, because the number 0 is an integer value, whereas false is a boolean.
Incorrect usage
The equals sign is often misused in steps of a mathematical argument, when used to connect steps of working rather than to show equality. For example, if one was 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. A correct version of the argument would be 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, 10 + 5 = 15.
See also
Notes
- ^ From Latin gamellus, twin.
- ^ The MacTutor History of Mathematics archive
References
- Cajori, Florian (1993). A History of Mathematical Notations. New York: Dover (reprint). ISBN 0-486-67766-4.
- Boyer, C. B.: A History of Mathematics, 2nd ed. rev. by Uta C. Merzbach. New York: Wiley, 1989 ISBN 0-471-09763-2 (1991 pbk ed. ISBN 0-471-54397-7)
