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  2. Word problem (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Word_problem_(mathematics)

    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]

  3. Word equation - Wikipedia

    en.wikipedia.org/wiki/Word_equation

    A classical example of a word equation is the commutation equation =, in which is an unknown and is a constant word. It is well-known [ 4 ] that the solutions of the commutation equation are exactly those morphisms h {\displaystyle h} mapping x {\displaystyle x} to some power of w {\displaystyle w} .

  4. Word (group theory) - Wikipedia

    en.wikipedia.org/wiki/Word_(group_theory)

    This operation is known as reduction, and it does not change the group element represented by the word. Reductions can be thought of as relations (defined below) that follow from the group axioms. A reduced word is a word that contains no redundant pairs. Any word can be simplified to a reduced word by performing a sequence of reductions:

  5. List of undecidable problems - Wikipedia

    en.wikipedia.org/wiki/List_of_undecidable_problems

    Hilbert's tenth problem: the problem of deciding whether a Diophantine equation (multivariable polynomial equation) has a solution in integers. Determining whether a given initial point with rational coordinates is periodic, or whether it lies in the basin of attraction of a given open set, in a piecewise-linear iterated map in two dimensions ...

  6. Levi's lemma - Wikipedia

    en.wikipedia.org/wiki/Levi's_lemma

    If each unknown appears at most twice, then a word equation is called quadratic; in a quadratic word equation the graph obtained by repeatedly applying Levi's lemma is finite, so it is decidable if a quadratic word equation has a solution. [2] A more general method for solving word equations is Makanin's algorithm. [3] [4]

  7. 6 of the best and 6 of the worst Christmas movies on Netflix ...

    www.aol.com/6-best-6-worst-christmas-120901378.html

    The holiday season is incomplete for many people without holiday movies. This year, Netflix is streaming a wide range of Christmas classics and original movies.

  8. Closed-form expression - Wikipedia

    en.wikipedia.org/wiki/Closed-form_expression

    The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).

  9. ‘A truly good man’: Trump, Obama, Bush and Clinton pay ...

    www.aol.com/truly-good-man-trump-obama-004714602...

    Bill Clinton “Hillary and I mourn the passing of President Jimmy Carter and give thanks for his long, good life,” Clinton, the country's 42nd president, said in a statement on Sunday.

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