Re: Is a function a relation?

"David BL" <davidbl_at_iinet.net.au> wrote in message news:09f7bd9a-76f9-47c3-a4fd-8ef4556c2036_at_m19g2000yqk.googlegroups.com...
> On Jun 23, 1:09 pm, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
>>
>> You considered the wrong relation values having the wrong
>> attribute names. Here are the correct values
>>
>> f(x) = x+1 -> { (domain,range) | range = domain + 1 }
>> g(y) = y+1 -> { (domain,range) | range = domain - 1 }
>>
>> corresponding to the f(x) and g(y) you gave.
>
> So you're suggesting that a function is a relation where a special
> convention has been followed in the choice of attribute names? Yes
> that's one way of looking at it. That would in fact suggest the
> interesting idea that one can use the RA to define functions. E.g.
> start with some n-ary relation and use projection to get a binary
> relation, and rename as required according to this special naming
> convention.

I think that it is not names but roles. Instead of domain and range, think determinant and dependent. A function is a relation that has defined in its schema at least one dependent attribute that does not belong to all determinants. Put it another way: a function is a relation that satisfies at least one nontrivial functional dependency. Received on Tue Jun 23 2009 - 14:32:46 CEST