Re: Examples for one-to-one associations?

"partial injective function"

On Jun 8, 9:29 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> Keith H Duggar wrote:
> > On Jun 7, 2:25 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>
> >>Gene Wirchenko wrote:
>
> >>>On Sat, 5 Jun 2010 20:49:59 -0700 (PDT), hoodwill
> >>><chase.saund..._at_gmail.com> wrote:
>
> >>>>Examples of one to ones:
>
> >>>>1) Spouse
>
> >>>     You need a time element.  Even given monogamy, many people have
> >>>been married more than once.
>
> >>Even more basic than that: Some folks are single.
>
> > Why is that an issue? If a person is single then they would not appear
> > in the Spouse relation. one-to-one relations can be partial can they
> > not?
>
> The relative cardinality is 1:zero-or-one not 1:1.

I don't think that is correct. The cardinality is defined by the domain definitions of the relation, not by the current extent of the relation. Further, since we are not dealing with multivalued theory the cardinality is never of the form "C1:C2 or C1:C3 ..." for a particular domain and relation (where C# are cardinals); rather it is fixed at some C1:C2 regardless of the current extension.

As far as I know, in mathematics the properties "injective" (ie one-to-one) and "partial" are not mutually exclusive. Please Google "partial injective function" to find both definitions and examples of such functions. For example, the square root function over the natural numbers is considered a partial injective function.

KHD Received on Fri Jun 18 2010 - 17:07:34 CEST