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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.
This same conception can be found in subsequent grammars, such as 1878's A Tamil Grammar [8] or 1882's Murby's English grammar and analysis, where the conception of an X phrase is a phrase that can stand in for X. [9] By 1912, the concept of a noun phrase as being based around a noun can be found, for example, "an adverbial noun phrases is a ...
For example, the noun phrase kinesiology functions as a pre-head complement in the larger noun phrase a kinesiology student. The noun phrase's status a complement can be made clearer by paraphrasing the noun phrase that contains it: a student of kinesiology , in which of kinesiology is more clearly a complement.
An example of the second case is the decidability of the first-order theory of the real numbers, a problem of pure mathematics that was proved true by Alfred Tarski, with an algorithm that is impossible to implement because of a computational complexity that is much too high. [122]
The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes. There are two canonical proofs that are always used to show non-mathematicians what a mathematical proof is like:
For example one might decide that is the normal form of () /, (/), and (/), and devise a transformation system to rewrite those expressions to that form, in the process proving that all equivalent expressions will be rewritten to the same normal form. [2] But not all solutions to the word problem use a normal form theorem - there are algebraic ...