Definition talk:Graph of Real Function

We've got Real Function defined as a mapping whose domain and codomain are $\R$ rather than $\R^m$ and $\R^n$ and so on. This is how it is defined in the sources I have available to me. However, I am wondering more and more how essential it is that the a "Real Function" should in fact be constrained to be one-dimensional.

Obviously in the context of manifolds, where the multidimensionality of the domain and codomain are of great importance, this makes immediate sense, but there's probably a danger of confusing those of a less advanced stage.

My gut feeling is to refer to such multidimensional "real functions" just as mappings like everything else which is not a "real function" or a "real-valued function" or "complex function" etc., which would make it perhaps better to subsume the the page "Graph of Real Function" into "Graph of Mapping", and reserve the name "Graph of Real Function" to the specific case where the codomain is genuinely just $\R$.

It's all the same in the end: it's the subset of the cartesian product which defines the correspondence between the domain and codomain, whatever the latter are. --prime mover (talk) 22:11, 12 April 2021 (UTC)
 * Fine with me. We can have it under graph of mappings. We also have Definition:Real Multivariable Function and Definition:Vector-Valued Function, so maybe we should call it Graph of Real Multivariable Vector-Valued Function? Extra words should signal that this is not just a simple function everybody is used to.--Julius (talk) 06:16, 13 April 2021 (UTC)


 * Perhaps the bigger question is: why bother to have a separate definition at all? It's just the graph of a mapping applied to a specific domain. Perhaps make it a subpage or an example of a graph of a mapping. IMO it's important to stress that all these things are the same sort of thing.


 * One reason for having a separate page for the graph of a real function $f: \R \to \R$ or $f: S \to \R$ where $S \subseteq \R$ is that you can conveniently present a picture of it as the "canonical" graph that is presented to children in grade school -- hence providing the link to a page which is understood at elementary level -- but by the time you get to manifolds, you are probably going to be familiar with general mappings. --prime mover (talk) 06:32, 13 April 2021 (UTC)