An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Logic and Philosophy, proposition refers to either (a the content or Meaning of a meaningful Declarative sentence This is a listing of common symbols found within all branches of the science of Mathematics. Equations are written with an equal sign, as in

2 + 3 = 5. History The "=" symbol that is now universally accepted by mathematics for equality was first recorded by Welsh mathematician Robert Recorde in The

The equation above is an example of an equality: a proposition which states that two constants are equal. Equality is the paradigmatic example of the more general concept of Equivalence relations on a set those binary relations which are reflexive, symmetric In Logic and Philosophy, proposition refers to either (a the content or Meaning of a meaningful Declarative sentence Equalities may be true or false.

Equations are often used to state the equality of two expressions containing one or more variables. In mathematics the word expression is a term for any well-formed combination of mathematical symbols A variable (ˈvɛərɪəbl is an Attribute of a physical or an abstract System which may change its Value while it is under Observation. In the reals we can say, for example, that for any given value of x it is true that

x(x − 1) = x² − x. In Mathematics, the real numbers may be described informally in several different ways

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. In Mathematics, the term identity has several different important meanings An identity is an equality that remains true regardless of the values of Logic is the study of the principles of valid demonstration and Inference. The following equation is not an identity:

x² − x = 0.

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. This article is about the zeros of a function which should not be confused with the value at zero. 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. In Mathematics, equation solving is the problem of finding what values ( Numbers functions, sets, etc

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,

(x + 1)² = x² + 2x + 1

is an identity, while

(x + 1)² = 2x² + x + 1

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.

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. A variable (ˈvɛərɪəbl is an Attribute of a physical or an abstract System which may change its Value while it is under Observation.

Properties

If an equation in algebra is known to be true, the following operations may be used to produce another true equation:

1. Any quantity can be added to both sides. Elementary algebra is a fundamental and relatively basic form of Algebra taught to students who are presumed to have little or no formal knowledge of Mathematics beyond Addition is the mathematical process of putting things together
2. Any quantity can be subtracted from both sides. Subtraction is one of the four basic Arithmetic operations it is the inverse of Addition, meaning that if we start with any number and add any number and then subtract
3. Any quantity can be multiplied to both sides.
4. Any nonzero quantity can divide both sides. In Mathematics, especially in elementary Arithmetic, division is an arithmetic operation which is the inverse of Multiplication.
5. Generally, any function can be applied to both sides. The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function (However, caution must be exercised to ensure that one does not encounter extraneous solutions. In Mathematics, an extraneous solution represents a solution such as that to an equation that emerges from the process of solving the problem but is not a valid solution )

The algebraic properties (1-4) imply that equality is a congruence relation for a field; in fact, it is essentially the only one. See Congruence (geometry for the term as used in elementary geometry In Abstract algebra, a field is an Algebraic structure in which the operations of Addition, Subtraction, Multiplication and division

The most well known system of numbers which allows all of these operations is the real numbers, which is an example of a field. In Mathematics, the real numbers may be described informally in several different ways In Abstract algebra, a field is an Algebraic structure in which the operations of Addition, Subtraction, Multiplication and division However, if the equation were based on the natural numbers for example, some of these operations (like division and subtraction) may not be valid as negative numbers and non-whole numbers are not allowed. In Mathematics, a natural number (also called counting number) can mean either an element of the set (the positive Integers or an The integers are an example of an integral domain which does not allow all divisions as, again, whole numbers are needed. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French In Abstract algebra, a branch of Mathematics, an integral domain is a Commutative ring with an additive identity 0 and a multiplicative identity 1 such However, subtraction is allowed, and is the inverse operator in that system. In Mathematics, if &fnof is a function from A to B then an inverse function for &fnof is a function in the opposite direction from B

If a function that is not injective is applied to both sides of a true equation, then the resulting equation will still be true, but it may be less useful. Formally, one has an implication, not an equivalence, so the solution set may get larger. The material conditional, also known as the material implication or truth functional conditional, expresses a property of certain Conditionals in Logic In Logic and Mathematics, logical biconditional (sometimes also known as the material biconditional) is a Logical operator connecting two statements The functions implied in properties (1), (2), and (4) are always injective, as is (3) if we do not multiply by zero. Some generalized products, such as a dot product, are never injective. In Mathematics, a product is the Result of multiplying, or an expression that identifies factors to be multiplied In Mathematics, the dot product, also known as the scalar product, is an operation which takes two vectors over the Real numbers R

See also

External links

• Mathematical equation plotter: Plots 2D mathematical equations, computes integrals, and finds solutions online. In Mathematics, an inequation is a statement that two objects or expressions are not the same or do not represent the same value In Mathematics, an inequality is a statement about the relative size or order of two objects or about whether they are the same or not (See also equality A linear equation is an Algebraic equation in which each term is either a Constant or the product of a constant and (the first power of a single Variable In Mathematics, a quadratic equation is a Polynomial Equation of the second degree. This article discusses cubic equations in one variable For a discussion of cubic equations in two variables see Elliptic curve. In Mathematics, a quartic equation is one which can be expressed as a Quartic function equalling zero In Mathematics, a quintic equation is a Polynomial Equation of degree five An indeterminate equation, in Mathematics, is an equation for which there is an infinite set of solutions for example 2x = y is a simple indeterminate equation A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the In Mathematics, an integral equation is an equation in which an unknown function appears under an Integral sign In Mathematics or its applications a functional equation is an Equation expressing a relation between the value of a function (or functions at a point with its values In Mathematics, a Diophantine equation is an indeterminate Polynomial Equation that allows the variables to be Integers only This is a list of Equations, by Wikipedia page See also List of equations in classical mechanics, List of relativistic equations, Equation solving In Mathematics, the theory of equations comprises a major part of traditional Algebra. In Mathematics, parametric equations are a method of defining a curve In Mathematics, a polynomial is an expression constructed from Variables (also known as indeterminates and Constants using the operations This is a list of scientific equations named after people (eponymous equations
• Equation plotter: A web page that can plot general equations, not just functions.
• WZGrapher: A Windows freeware program that plots Cartesian and polar equations, with both integration and differentiation solvers and graphing capabilities. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change
• Equation Wizard: Automatic algebraic equation solver
• EqWorld — contains information on solutions to many different classes of mathematical equations.
• EquationSolver: A webpage that can solve single equations and linear equation systems.
• WebGraphing.com: Online Equation Plotter with Automatic Table of Coordinates
• Equation Solver: Automatic algebraic equation solver