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While the word problem asks whether two terms containing constants are equal, a proper extension of the word problem known as the unification problem asks whether two terms , containing variables have instances that are equal, or in other words whether the equation = has any solutions.
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Word equations are a central object in combinatorics on words; they play an analogous role in this area as do Diophantine equations in number theory. One stark difference is that Diophantine equations have an undecidable solubility problem, [2] whereas the analogous problem for word equations is decidable. [3]
The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for ...
Solving an equation symbolically means that expressions can be used for representing the solutions. For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement.
A variable may denote an unknown number that has to be determined; in which case, it is called an unknown; for example, in the quadratic equation ax 2 + bx + c = 0, the variables a, b, c are parameters, and x is the unknown. Sometimes the same symbol can be used to denote both a variable and a constant, that is a well defined mathematical object.