Wiktionary
n. 1 A mathematics question that states verbally what is usually written using symbols (or, for geometry, in a picture). 2 (context mathematics English) A question of whether an element of a certain group (or monoid or the like) is the identity, given an obscure representation of that element.
Wikipedia
In mathematics education, the term word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are occasionally also referred to as story problems and may vary in the amount of language used.
In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set. The problem is commonly encountered in abstract algebra, where given a presentation of an algebraic structure by generators and relators, the problem is to determine if two expressions represent the same element; a prototypical example is the word problem for groups. Less formally, the word problem in an algebra is: given a set of identities E, and two expressions x and y, is it possible to transform x into y using the identities in E as rewriting rules in both directions? While answering this question may not seem hard, the remarkable (and deep) result that emerges, in many important cases, is that the problem is undecidable.
Many, if not most all, undecidable problems in mathematics can be posed as word problems; see the list of undecidable problems for many examples.
The term word problem has several meanings:
- word problem (mathematics education) is a type of textbook problem designed to help students apply abstract mathematical concepts to "real-world" situations
- word problem (mathematics) is a decision problem for algebraic identities in mathematics and computer science
- word problem for groups is the problem of recognizing the identity element in a finitely presented group
- word problem (computability) is a decision problem concerning formal languages
Usage examples of "word problem".
Both of them looked as if they were struggling with a difficult word problem.
It was a word problem, about Jack and Jill renting a rowboat and how much it would cost them if they rowed for two and a half hours.
I've scanned the contents: a hundred-word problem, condensed to about ten-thousand.