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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.
A word sort is a developmental word study activity espoused by the Words Their Way curriculum as written by Donald R. Bear, Marcia Invernizzi, Shane Templeton, and Francine Johnston. The activity focuses students' attention on critical features of words, namely sound, pattern, and meaning.
The proof is difficult to follow but marks a turning point in the word problem for groups. [3]: 342 1955 (): Pyotr Novikov gives the first published proof that the word problem for groups is unsolvable, using Turing's cancellation semigroup result. [17] [3]: 354 The proof contains a "Principal Lemma" equivalent to Britton's Lemma.
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Related problems include approximate sorting (sorting a sequence to within a certain amount of the correct order), partial sorting (sorting only the k smallest elements of a list, or finding the k smallest elements, but unordered) and selection (computing the kth smallest element). These can be solved inefficiently by a total sort, but more ...
The word problem was one of the first examples of an unsolvable problem to be found not in mathematical logic or the theory of algorithms, but in one of the central branches of classical mathematics, algebra. As a result of its unsolvability, several other problems in combinatorial group theory have been shown to be unsolvable as well.
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