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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.
In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups , but there are many other instances as well.
Then the word problem in is solvable: given two words , in the generators of , write them as words in and compare them using the solution to the word problem in . It is easy to think that this demonstrates a uniform solution of the word problem for the class K {\displaystyle K} (say) of finitely generated groups that can be embedded in G ...
The Knuth–Bendix completion algorithm (named after Donald Knuth and Peter Bendix [1]) is a semi-decision [2] [3] algorithm for transforming a set of equations (over terms) into a confluent term rewriting system. When the algorithm succeeds, it effectively solves the word problem for the specified algebra.
A decision problem P is said to be complete for a set of decision problems S if P is a member of S and every problem in S can be reduced to P. Complete decision problems are used in computational complexity theory to characterize complexity classes of decision problems. For example, the Boolean satisfiability problem is complete for the class ...
A subset S of a group G is called a generating set if every element of G can be represented by a word in S. When S is not a generating set for G , the set of elements represented by words in S is a subgroup of G , known as the subgroup of G generated by S and usually denoted S {\displaystyle \langle S\rangle } .
On the row beneath “Pay to the order of,” write the payment amount in words. Sign your name on the line in the bottom right. Write a brief description on the “memo” line at the bottom left ...
Word problem (mathematics education), a type of textbook exercise or exam question to have students apply abstract mathematical concepts to real-world situations; Word problem (mathematics), a decision problem for algebraic identities in mathematics and computer science; Word problem for groups, the problem of recognizing the identity element ...