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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.
A word equation is a formal equality:= = between a pair of words and , each over an alphabet comprising both constants (c.f. ) and unknowns (c.f. ). [1] An assignment of constant words to the unknowns of is said to solve if it maps both sides of to identical words.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
As a theme and as a subject in the arts, the anti-intellectual slogan 2 + 2 = 5 pre-dates Orwell and has produced literature, such as Deux et deux font cinq (Two and Two Make Five), written in 1895 by Alphonse Allais, which is a collection of absurdist short stories; [1] and the 1920 imagist art manifesto 2 × 2 = 5 by the poet Vadim ...
Solving an equation symbolically means that expressions can be used for representing the solutions. For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement.
The seven selected problems span a number of mathematical fields, namely algebraic geometry, arithmetic geometry, geometric topology, mathematical physics, number theory, partial differential equations, and theoretical computer science. Unlike Hilbert's problems, the problems selected by the Clay Institute were already renowned among ...
Problems 1, 2, 5, 6, [a] 9, 11, 12, 15, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems. That leaves 8 (the Riemann hypothesis), 13 and 16 [b] unresolved. Problems 4 and 23 are considered as too vague to ever be described as solved; the withdrawn 24 would also be in ...