mathematical statement that asserts the equality of two expressions
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A mathematical equation is an expression containing two mathematical objects connected by an equals sign (=) . The equals sign says that both sides are exactly equal, or of the same value. An equation can be as simple as x=0, or as complex as or harder.
There are two kinds of mathematical equations:
- The kind of equation that is either true or false; these are also called identities. For example:
- The kind of equation that is only true for certain values of the variable(s). The equation is only true if the variable(s) have that value. For example:
The second kind is often used to solve problems in which finding the value of some variables is involved. For example, if
The second kind of equation is used in algebra. For example, to solve the equation 2x = 8 for x, one would follow an algebraic rule to find that x = 4.
Types of equationsEdit
Equations can be classified by the types of operations and quantities involved. For example:
- An algebraic equation is an equation in which both sides are polynomials. These are further classified by degree:
- Linear equation for degree one
- Quadratic equation for degree two
- Cubic equation for degree three
- Quartic equation for degree four
- Quintic equation for degree five
- A Diophantine equation is an equation where the unknowns are required to be integers
- A differential equation is a functional equation involving derivatives of the unknown functions, which include:
- ↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-09-01.
- ↑ "Equations and Formulas". www.mathsisfun.com. Retrieved 2020-09-01.
- ↑ "A statement of equality between two expressions. Equations are of two types, identities and conditional equations (or usually simply "equations")". « Equation », in Mathematics Dictionary, Glenn James et Robert C. James (éd.), Van Nostrand, 1968, 3 ed. 1st ed. 1948, p. 131.
- ↑ Une équation est une égalité entre deux expressions mathématiques, donc une formule de la forme A = B, où les deux membres A et B de l'équation sont des expressions où figurent une ou plusieurs variables, représentées par des lettres. ÉQUATION, mathématique - Encyclopædia Universalis