Equals

Mathematical concept of equality

Template:Infobox mathematical concept Equality is a fundamental concept in mathematics, denoted by the symbol = (equals sign). It asserts that two expressions represent the same quantity or value. Equality is a binary relation, meaning it involves two entities that are being compared.

Definition

In mathematics, equality is defined as a relationship between two expressions, stating that they are the same in value or represent the same mathematical object. For example, the equation \(2 + 2 = 4\) asserts that the sum of 2 and 2 is equal to 4.

Properties

Equality has several important properties that are used in various mathematical contexts:

• Reflexive property: For any mathematical object \(a\), \(a = a\).
• Symmetric property: If \(a = b\), then \(b = a\).
• Transitive property: If \(a = b\) and \(b = c\), then \(a = c\).

These properties are essential in proving various mathematical theorems and in solving equations.

Applications

Equality is used extensively in different branches of mathematics, including:

• Algebra: Solving equations and inequalities.
• Geometry: Establishing congruence and similarity between shapes.
• Calculus: Defining limits, derivatives, and integrals.
• Number theory: Proving properties of numbers and their relationships.

Equals Sign

The equals sign (=) is a symbol used to indicate equality. It was first introduced by the Welsh mathematician Robert Recorde in 1557 in his book "The Whetstone of Witte". Recorde chose the symbol because "no two things can be more equal".

Related Concepts

• Inequality (mathematics)
• Equation
• Identity (mathematics)
• Equivalence relation

See Also

• Mathematical notation
• Logic
• Set theory
• Proof (mathematics)