Noun

Singular equation

Plural equations

equation (plural equations)

1. (mathematics) An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
2. (astronomy) A small correction to observed values to remove the effects of systematic errors in an observation.

Derived terms

• algebraic equation
• Arrhenius equation
• chemical equation
• differential equation
• Diophantine equation
• Drake equation
• integral equation
• Kepler's equation
• Lagrange's equations
• linear equation

• Navier-Stokes equation
• parametric equation
• partial differential equation
• Pell's equation
• personal equation
• polynomial equation
• quadratic equation
• Schrödinger's wave equation
• Van der Waals equation
• wave equation

Related terms

• equality
• equational
• identity
• inequation
• inequality

An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are written with an equal sign, as in

The equations above are examples of an equality: a proposition which states that two constants are equal. Equalities may be true or false.

Equations are often used to state the equality of two expressions containing one or more variables. In the reals we can say, for example, that for any given value of x it is true that

The equation above is an example of an identity, that is, an equation that is true regardless of the values of any variables that appear in it. The following equation is not an identity:

It is false for an infinite number of values of x, and true for only two, the roots or solutions of the equation, x = 0 and x = 1. Therefore, if the equation is known to be true, it carries information about the value of x. To solve an equation means to find its solutions.

Many authors reserve the term equation for an equality which is not an identity. The distinction between the two concepts can be subtle; for example,

is an identity, while

is an equation, whose roots are x = 0 and x = 1. Whether a statement is meant to be an identity or an equation, carrying information about its variables can usually be determined from its context; or by making a distinction between the equality sign ( = ) for a statement not true except perhaps in particular situations, and the equivalence symbol () for statements know to be true without further specification.

Letters from the beginning of the alphabet like a, b, c... often denote constants in the context of the discussion at hand, while letters from end of the alphabet, like x, y, z..., are usually reserved for the variables, a convention initiated by Descartes.