# Re: what are keys and surrogates?

Date: Sun, 13 Jan 2008 23:25:32 +0100

Message-ID: <478a8f80$0$85781$e4fe514c_at_news.xs4all.nl>

David BL schreef:

> Keith H Duggar wrote:

>> David BL wrote: >>> Keith H Duggar wrote: >>>> David BL wrote: >>>>> Marshall wrote: >>>>>> An interesting note, by the way: >>>>>> functions are relations ... >>>>> Isn't it more precise to say that the graph of a >>>>> function is a relation? >>>> No, it isn't. >>>> http://mathworld.wolfram.com/Function.html >>> From mathworld a relation >>> http://mathworld.wolfram.com/Relation.html >>> is defined as a subset of a cartesian product. If a >>> function is a relation why do they define a graph of >>> a function f as >>> { (x,f(x)) | x in domain of f }, >>> as described in >>> http://mathworld.wolfram.com/FunctionGraph.html[snip]

> ... Wikipedia for example defines "graph of

*> function" without any such restriction*

*>*

*> http://en.wikipedia.org/wiki/Function_%28mathematics%29*

*>*

*> http://en.wikipedia.org/wiki/Graph_of_a_function*

[snip]

Quoted from there:

"In mathematics, the graph of a function f is the collection of
all ordered pairs (x,f(x)). In particular, graph means the
graphical representation of this collection, in the form
of a curve or surface, together with axes, etc."

ISTM this is what I use the word 'plot' for.

Also from that page (at the start):

"For another use of the term "graph" in mathematics,
see graph theory".

In dutch 'grafiek' is a 'plot' (or 'chart'), and 'graph' (another word) is a 'collection of edges and nodes' - maybe it boils down to a homonym problem in english?

> This however doesn't change the fact that most authors define a

*> (mathematical) relation as a set of ordered tuples, which means a
**> function is not a relation (assuming, as most do, that a function has
**> a defined domain and codomain).
*

?

How does having a domain and a codomain stops a function from being a kind of relation ? (David Cressey asked a similar question).

> Furthermore, I was correct when I

*> stated that a graph of a function is a relation, according to the more
**> general definition of graph of function, as described in Wikipedia.
*

Is it more general?

Maybe so.

Anyway, what is wrong with using 'plot' for this, in order to
disambiguate - is there some meaning lost?

-- What you see depends on where you stand.Received on Sun Jan 13 2008 - 23:25:32 CET