It was invented in 1557 by Robert Recorde. In Unicode and ASCII, it has the code point U+003D. In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value. The equals sign ( British English) or equal sign ( American English), also known as the equality sign, is the mathematical symbol =, which is used to indicate equality in some well-defined sense. Then the axiom of extensionality states that two equal sets are contained in the same sets.A well-known equality featuring the equal sign In first-order logic without equality, two sets are defined to be equal if they contain the same elements. "The reason why we take up first-order predicate calculus with equality is a matter of convenience by this we save the labor of defining equality and proving all its properties this burden is now assumed by the logic." Set equality based on first-order logic without equality Incorporating half of the work into the first-order logic may be regarded as a mere matter of convenience, as noted by Lévy.
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