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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 fact can be defined as something that is the case, in other words, a state of affairs. [13] [14] Facts may be understood as information, which makes a true sentence true: "A fact is, traditionally, the worldly correlate of a true proposition, a state of affairs whose obtaining makes that proposition true."
The Problem Child, Rebel, or Truth Teller: [13] the child who a) causes most problems related to the family's dysfunction or b) "acts out" in response to preexisting family dysfunction, in the latter case often in an attempt to divert attention paid to another member who exhibits a pattern of similar misbehavior.
The Ages of Three Children puzzle (sometimes referred to as the Census-Taker Problem [1]) is a logical puzzle in number theory which on first inspection seems to have insufficient information to solve. However, with closer examination and persistence by the solver, the question reveals its hidden mathematical clues, especially when the solver ...
The Colley family was then up, with one contestant, Drake, noting that Harry has red hair – which was the third most common fact about him amongst Americans. The board then revealed the fifth ...
[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics". [8] However, though the Collatz conjecture itself remains open, efforts to solve the problem have led to new techniques and many partial results. [8] [9]
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