> Quoth Evan Keel:
>
[quoted text clipped - 8 lines]
>
> No. There may be dependencies where the left side is empty.
In that case the declared candidate key is not really a candidate
key. Under the assumption that the declared candidate keys are indeed
candidate keys, the claim is correct.
> But it's a
> common mistake. If I remember correctly, one of my database textbooks
> "proves" that any relvar with just two attributes is automatically in BCNF.
Under the assumption that I just mentioned, that claim is actually
also correct.
-- Jan Hidders
David Cressey - 07 Sep 2007 15:19 GMT
> > Quoth Evan Keel:
> >
[quoted text clipped - 12 lines]
> key. Under the assumption that the declared candidate keys are indeed
> candidate keys, the claim is correct.
I'm really confused by the above. First off, if there were a dependency
where the left side is empty, wouldn't the same value have to exist the
dependent column, for all of the rows?
> > But it's a
> > common mistake. If I remember correctly, one of my database textbooks
[quoted text clipped - 4 lines]
>
> -- Jan Hidders
Jan Hidders - 07 Sep 2007 20:35 GMT
> > > Quoth Evan Keel:
>
[quoted text clipped - 22 lines]
> where the left side is empty, wouldn't the same value have to exist the
> dependent column, for all of the rows?
Yes. But as Brian correctly pointed out, what I said in the above was
wrong. In fact my remark about binary relations in BCNF is also not
correct. For example R(A,B) with FD {}-->B is not in BCNF. Not my day,
apparently. :-(
-- Jan Hidders
Brian Selzer - 07 Sep 2007 18:40 GMT
>> Quoth Evan Keel:
>>
[quoted text clipped - 15 lines]
> key. Under the assumption that the declared candidate keys are indeed
> candidate keys, the claim is correct.
That's not true, Jan, consider:
{A, B, C} | A --> B /\ {} --> C
If {} --> C holds, then A --> C also holds.
Since A --> B /\ A --> C, then A --> BC.
{{A:1, B:2, C:1}
{A:2, B:4, C:1}
{A:3, B:4, C:1}
{A:4, B:3, C:1}}
Clearly A is the only candidate key, even though the FD {} --> C holds.
>> But it's a
>> common mistake. If I remember correctly, one of my database textbooks
[quoted text clipped - 5 lines]
>
> -- Jan Hidders
Jan Hidders - 07 Sep 2007 20:29 GMT
> >> Quoth Evan Keel:
>
[quoted text clipped - 29 lines]
>
> Clearly A is the only candidate key, even though the FD {} --> C holds.
Indeed, I stand corrected.
-- Jan Hidders