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Elegant variation is the attempt to relieve repetition by replacing words with synonyms. For example: "Three homes were destroyed by a five-alarm fire yesterday. Neighbors reported the blaze about 4 pm. Two firefighters were injured battling the inferno. Officials called the conflagration suspicious." "Pope Paul waved from the balcony.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
The word problem is a well-known example of an undecidable problem. If A {\displaystyle A} is a finite set of generators for G {\displaystyle G} , then the word problem is the membership problem for the formal language of all words in A {\displaystyle A} and a formal set of inverses that map to the identity under the natural map from the free ...
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.
Examples to show the effectiveness of word-based approaches are usually drawn from fusional languages, where a given "piece" of a word, which a morpheme-based theory would call an inflectional morpheme, corresponds to a combination of grammatical categories, for example, "third-person plural". Morpheme-based theories usually have no problems ...
Sleeping Beauty problem: A probability problem that can be correctly answered as one half or one third depending on how the question is approached. Three Prisoners problem , also known as the Three Prisoners paradox: [ 3 ] A variation of the Monty Hall problem .