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The word problem was one of the first examples of an unsolvable problem to be found not in mathematical logic or the theory of algorithms, but in one of the central branches of classical mathematics, algebra. As a result of its unsolvability, several other problems in combinatorial group theory have been shown to be unsolvable as well.
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]
For example, the Institute for Creation Research, in order to imply placement of evolution in the category of 'religions', including atheism, fascism, humanism and occultism, commonly uses the words evolutionism and evolutionist to describe the consensus of mainstream science and the scientists subscribing to it, thus implying through language ...
Evolution is the change in the heritable characteristics of biological populations over successive generations. [1] [2] It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, resulting in certain characteristics becoming more or less common within a population over successive generations. [3]
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 brain allows an individual to recognize patterns, perceive speech, develop strategies to circumvent ecologically-based problems such as foraging for food, and also permits the phenomenon of color vision. It is said that in humans and primates the neocortex is responsible for reasoning and consciousness.
The 4 Nations Face-Off championship between USA and Canada on Thursday night drew a significant audience for ESPN's broadcast.. Canada's 3-2 victory over USA in overtime averaged 9.3 million ...
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: