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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]
Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
The word problem asks whether two words are effectively the same group element. By relating the problem to Turing machines , one can show that there is in general no algorithm solving this task. Another, generally harder, algorithmically insoluble problem is the group isomorphism problem , which asks whether two groups given by different ...
Normally, roman upright typeface is not used for symbols, except for symbols representing a standard function, such as the symbol "" of the sine function. [2] In order to have more symbols, and for allowing related mathematical objects to be represented by related symbols, diacritics, subscripts and superscripts are often used.
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Given a set V of variable symbols, a set C of constant symbols and sets F n of n-ary function symbols, also called operator symbols, for each natural number n ≥ 1, the set of (unsorted first-order) terms T is recursively defined to be the smallest set with the following properties: [1] every variable symbol is a term: V ⊆ T,
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.