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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]
An idiom is a common word or phrase with a figurative, non-literal meaning that is understood culturally and differs from what its composite words' denotations would suggest; i.e. the words together have a meaning that is different from the dictionary definitions of the individual words (although some idioms do retain their literal meanings – see the example "kick the bucket" below).
Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example is Fermat's Last Theorem . This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles , who used tools including scheme theory from algebraic geometry , category ...
The energy that a physical body possesses due to its motion, defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. The body continues to maintain this kinetic energy unless its velocity changes. Contrast potential energy. Kirchhoff's circuit laws. Also called Kirchhoff's rules or simply Kirchhoff's laws.
For example, squares (resp. triangles) have 4 sides (resp. 3 sides); or compact (resp. Lindelöf) spaces are ones where every open cover has a finite (resp. countable) open subcover. sharp Often, a mathematical theorem will establish constraints on the behavior of some object; for example, a function will be shown to have an upper or lower bound.