# Re: what are keys and surrogates?

From: mAsterdam <mAsterdam_at_vrijdag.org>
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

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