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| ``Re: Ambiguity with Graph Theory''
by rspuzio on 2005-06-08 11:05:28 |
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| Unfortunately, there are ambiguitites like this where the same word refers to more than one concept all over mathematics. For another example, the term "field" can refer to set of objects which are closed under addition, subtraction , multiplication, and division, or to the assignment of a geometric object such as a vector to every point of a manifold.
I really don't think that imposing a renaming convention such as you suggest would work since these terms are too deeply ingrained. You would have to go back and rewrite the mathematical literature and persuade mathematicians to make the change. Also, writing "graph of a function" all the tome can get clumsy, especially when "of a function" is clear from the context.
Rather, what happens is that the ambiguity is lifted by context --- one meaning is used in one field of mathematics and the other in another field. (Yet a third ambiguity --- the term "field" can also be used in a non-technical sense!) We can implement that on Planet Math by a classification-steered linking which will choose between the definition based on the subject of the material in which the term occurs. Sometimes, there arise contexts in which both senses of an unambiguous word may occur. In this case, using more descripiptive phrases like 'graph of a function' could be of use when it is not obvious from the context which of the two meanings is intended.
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