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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]
The following articles contain lists of problems: List of philosophical problems; List of undecidable problems; Lists of unsolved problems; List of NP-complete problems;
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 ...
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:
Microsoft Copilot in Windows supports the use of voice commands. By default, it is accessible via the Windows taskbar. [95] Copilot in Windows is also able to provide information on the website currently being browsed by a user in Microsoft Edge. [96] In 2024, Microsoft began to establish standards for "AI PCs" powered by Windows 11.
Copy the table to a wiki sandbox. In Calc select the table. Copy directly from it, and then paste into the visual editor, or if that does not work, into a blank visual editor table where the first header cell has been selected. It may take up to a minute. If there is a problem, then paste into Excel2Wiki first, and copy the wikitext.