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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]
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.
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 ...
The problem is that we divided both sides by , which involves the indeterminate operation of dividing by zero when = It is generally possible (and advisable) to avoid dividing by any expression that can be zero; however, where this is necessary, it is sufficient to ensure that any values of the variables that make it zero also fail to satisfy ...
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 ...
WordNet is a lexical database of semantic relations between words that links words into semantic relations including synonyms, hyponyms, and meronyms. The synonyms are grouped into synsets with short definitions and usage examples. It can thus be seen as a combination and extension of a dictionary and thesaurus.
The observer pattern addresses the following problems: [2] A one-to-many dependency between objects should be defined without making the objects tightly coupled. When one object changes state, an open-ended number of dependent objects should be updated automatically. An object can notify multiple other objects.