equals

Equals is a fundamental relation in mathematics and related fields that asserts that two expressions denote the same value. If a and b are equals, we write a = b. The symbol signals that the expressions on both sides represent an identical quantity or object in the given context.

Origin and symbol: The equals sign was introduced in 1557 by Robert Recorde in The Whetstone of Witte, who chose two parallel lines to denote that the expressions on either side are equal. The symbol has since become standard across arithmetic, algebra, and beyond.

In mathematics, equality is a binary relation with specific properties: reflexive (a = a); symmetric (if a = b, then b = a); transitive (if a = b and b = c, then a = c). It supports substitution: if a = b, then a can be replaced by b in any expression without changing value.

In mathematics there are also notions such as identity (a = a by necessity) and congruence (a ≡ b mod n) which relate to equality in particular structures. Equality can be exact or approximate in numerical work, requiring tolerance when dealing with real numbers or floating-point arithmetic.

In computer science, the equals sign is used differently across languages. It often denotes assignment rather than comparison; many languages use == to test equality, while others use a equals method to test object equality. Understanding the context is essential to interpreting a statement of equality.