Re: what are keys and surrogates?

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

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.