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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:
Then the word problem in is solvable: given two words , in the generators of , write them as words in and compare them using the solution to the word problem in . It is easy to think that this demonstrates a uniform solution of the word problem for the class K {\displaystyle K} (say) of finitely generated groups that can be embedded in G ...
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 ...
For example, the word "encyclopedia" is a sequence of symbols in the English alphabet, a finite set of twenty-six letters. Since a word can be described as a sequence, other basic mathematical descriptions can be applied. The alphabet is a set, so as one would expect, the empty set is a subset. In other words, there exists a unique word of ...
Formerly ClarisWorks Word Processing, also an older and unrelated application for Apple II. Succeeded by iWork. Amí: Windows: developed and marketed by Samna: Apple Writer: Apple II, Apple III: SuperWriter: Apricot Portable: Built-in word processor in Apricot Computers devices Authorea: word processor for students and researchers AstroType ...
Microsoft 365 is a family of productivity software, collaboration and cloud-based services, encompassing online services, products formerly marketed under Microsoft Office, and enterprise products and services. This list contains all the programs that are, or have been, in Microsoft Office since it was released for classic Mac OS in 1989, and ...
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