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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 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 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.
Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC.
Heading names of sections (including subsections) should be unique on a page. Using the same heading more than once on a page causes problems: An internal link (wikilink) to a section, in the form [[Article name#Section heading]], will link only to the first section on the page with that name, which may not be the intended target of the link.
An alphanumeric outline includes a prefix at the beginning of each topic as a reference aid. The prefix is in the form of Roman numerals for the top level, upper-case letters (in the alphabet of the language being used) for the next level, Arabic numerals for the next level, and then lowercase letters for the next level.
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. Kurt Gödel developed the concept for the proof of his incompleteness theorems .
A library bookshelf in Hong Kong classified using the New Classification Scheme for Chinese Libraries, an adaptation of the Dewey Classification scheme. The Dewey Decimal Classification (DDC), colloquially known as the Dewey Decimal System, is a proprietary library classification system which allows new books to be added to a library in their appropriate location based on subject.