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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.
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]
Word problem (mathematics education), a type of textbook exercise or exam question to have students apply abstract mathematical concepts to real-world situations; Word problem (mathematics), a decision problem for algebraic identities in mathematics and computer science; Word problem for groups, the problem of recognizing the identity element ...
The visible section or "overt" is the syntax that still remains in a sentence word. [15] Within sentence word syntax there are 6 different clause-types: Declarative (making a declaration), exclamative (making an exclamation), vocative (relating to a noun), imperative (a command), locative (relating to a place), and interrogative (asking a ...
The sentence can be given as a grammatical puzzle [7] [8] [9] or an item on a test, [1] [2] for which one must find the proper punctuation to give it meaning. Hans Reichenbach used a similar sentence ("John where Jack had...") in his 1947 book Elements of Symbolic Logic as an exercise for the reader, to illustrate the different levels of language, namely object language and metalanguage.
Gusty, a cartoon character created by the meteorologist Don Woods; Arthur Gusty and Mrs. Gusty, characters from the 1938 film Everything Happens to Me; Gusty and Baby Gusty, characters from the television series My Little Pony; Gusty, an elf character in Wee Sing: The Best Christmas Ever!
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.
Woods used Gusty to demonstrate how to be weather smart during thunderstorm and tornado activity. At various times, Gusty would also be drawn swimming, fishing, water skiing, or playing American football. Gusty was a responsible individual — raking leaves in the fall, mowing the grass in the summer, or sometimes just relaxing with a good book.