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One stark difference is that Diophantine equations have an undecidable solubility problem, [2] whereas the analogous problem for word equations is decidable. [ 3 ] A classical example of a word equation is the commutation equation x w = ⋅ w x {\displaystyle xw{\overset {\cdot }{=}}wx} , in which x {\displaystyle x} is an unknown and w ...
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.
Note that the rewriting here is one-way. The word problem is the accessibility problem for symmetric rewrite relations, i.e. Thue systems. [27] The accessibility and word problems are undecidable, i.e. there is no general algorithm for solving this problem. [28]
However, if one searches for real solutions, there are two solutions, √ 2 and – √ 2; in other words, the solution set is {√ 2, − √ 2}. When an equation contains several unknowns, and when one has several equations with more unknowns than equations, the solution set is often infinite. In this case, the solutions cannot be listed.
The problem, restricted to the case of an incompressible flow, is to prove either that smooth, globally defined solutions exist that meet certain conditions, or that they do not always exist and the equations break down. The official statement of the problem was given by Charles Fefferman. [13]
Known as word problems, they are used in mathematics education to teach students to connect real-world situations to the abstract language of mathematics. In general, to use mathematics for solving a real-world problem, the first step is to construct a mathematical model of the problem. This involves abstraction from the details of the problem ...