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A formal language is any set of symbols and combinations of symbols that people use to communicate information. [1] Some terminology relevant to the study of words should first be explained. First and foremost, a word is basically a sequence of symbols, or letters, in a finite set. [1] One of these sets is known by the general public as the ...
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.
A.R.T.'s robots have sabotaged a factory. The user must stop the noxious poisons from being released into the environment. There is a math problem that appears at the top the screen and four answers. Obviously, the user must select the correct answer before the barrel is over flow. Naturally, there are toxin puddles and tox-o-bots to avoid.
This operation is known as reduction, and it does not change the group element represented by the word. Reductions can be thought of as relations (defined below) that follow from the group axioms. A reduced word is a word that contains no redundant pairs. Any word can be simplified to a reduced word by performing a sequence of reductions:
Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary (pg.48). The problem states: Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk twice abreast.
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