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graph

Synonym: 
function graph
Type of Math Object: 
Definition
Major Section: 
Reference

Mathematics Subject Classification

03E20 no label found

Comments

I suggest that the noun graph should be defined as set of vertices and edges as in graph theory and that this entry should include function in the title. Maybe this should be called 'graph of a function'.

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.

I do not have a strong opinion on PlanetMath practive. My experience is that strong opinions are bad for Wiki based communities.

I would like to see graph in the sense of graph theory defined in Planet Math. How do you suggest that be done? I took a look at field and found it is defined here in the algebra sense not in the geometry sense; that is, it did not help me see a solution to multiple definitions of the same word.

Thank for your interaction. I assure you I approach PlanetMath with humility and good faith.

Cartan ( Scott Chastain )

Graph in the sense of graph theory defined in Planet Math:

http://planetmath.org/encyclopedia/Graph.html

As for the geomtry sense of the term "field", there are sevaral entries on scalar fields, vector fields, etc.

In cases like these where the same term can have several meanings, it would help to have disambiguation pages which point out that the word can be used in several ways, link to definitions of these different senses, and perhaps offer advice on how one can guess which meaning is being used or how to write so as to make it clear which meaning is intended. An example of such a page (as far as I know, it's the only one that has been written so far) is:

http://planetmath.org/encyclopedia/Orthogonal.html

It would be nice to have such entries for the terms "graph" and "field". In addition, once several such entries are written, it would be nice to great to make a glossary of ambiguous mathematical terms. As far as I know, such a reference does not exist, and it could prove of great service to the beleaguered math student who, knowing only of graphs of functions, opens a topology book and is puzzled by the use of the term "graph" found there.

Also, now that I think about it, it would be helpful for entries defining ambiguous terms to end with something like "For a different usage of the term "graph" in mathematics, look here." and refer the reader to the entry describing the other usage of the term. That would help make people aware that these terms are used in more than one sense and help unconfuse people.

Ok. I am glad to see graph in graph theory is defined. I apologize for not seeing this before.

If I try to following: type graph in upper right filed and hit the find button; I always get graph ( of a function ) and graph from graph theory is not in the found results. Do you understand why both definitions don't come up as top entries on from the find function?

Thanks again for you discussion time.

This sounds like a shortcoming of the search program. This should go on the list of improvements.

This sounds like a good idea; I had already thought of it, but it should
certainly be something automatic, so that authors won't have to keep updating
their entries when new definitions of similar terms appear.
It should be easy to implement, I guess.

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