Equals
In mathematics and logic, the term equals refers to the state of two expressions having the same value. The equals sign (=), introduced by Robert Recorde in 1557, is used to denote this relationship. Here are some key points about "equals":
- Symbol: The equals sign (=) is one of the most widely recognized symbols in mathematics. Robert Recorde chose this symbol because, as he wrote, "noe 2 thynges can be moare equalle."
- Mathematical Usage:
- It is used in equations where two expressions are set equal to each other, e.g., 2 + 2 = 4.
- It signifies equivalence or identity in algebra, logic, and set theory. For example, in set theory, A = B means that sets A and B contain exactly the same elements.
- In calculus, the equals sign can denote definitions, like f(x) = 2x + 1 where f(x) is defined as the function that maps x to 2x + 1.
- History:
- Before the equals sign, words like "is equal to" or "equals" were used to express equality. Recorde, in his book The Whetstone of Witte, first introduced the symbol to simplify mathematical writing.
- The equals sign has since become fundamental to the notation of mathematics, influencing not just mathematics but also computer science and programming.
- Logical Equivalence: In logic, "equals" often refers to logical equivalence, where two statements have the same truth value under all interpretations. This is typically denoted by ≡ or ⇔, but in simpler contexts, = might be used.
- Applications:
- Equations in algebra, where solving for variables involves manipulating expressions to maintain equality.
- Programming languages use the equals sign in various forms, often for assignment (e.g., `x = 5`) or comparison (e.g., `x == 5`).
- In database theory, equality is fundamental to join operations and key constraints.
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