Re: Do Data Models Need to built on a Mathematical Concept?

Neo wrote:

>>>>You need to learn is that a graph is equivalent to a binary
>>>>
>>>>
>relation,
>
>
>>>A graph is not equivalent to a binary relation.
>>>A graph is composed of binary relations.
>>>
>>>
>>...non-sense..
>>
>>
>
>It depends on your definition of a graph vs my definition of a binary
>relation. I define a binary relation as any two things that have
>something in common.
>
A (binary) relation is a subset of a Cartesian product.

What is a Cartesian product?

A familiar example is the Cartesian plane (the normal XY-plane) defined as the Cartesian product RxR (R=the set of real numbers).

It contains all possible points (x,y) where x and y belong to R

Now, a nice example of a relation is the unit circle, the set of points defined by
{(x,y) | x**2 + Y**2 = 1}. Clearly this set of points is just a subset of all points on the plane.

The interesting thing is that a Cartesian product contains as much information as a blank piece of paper, i.e. nothing. Only when we restrict ourselves to a subset of the points on the plane (e.g. by drawing the unit circle) do we have information.

It was the great insight of Ted Codd in 1970 that this way of thinking (that is ingrained in modern mathematics) can be applied to database technology.

regards,
Lauri Pietarinen Received on Sat May 03 2003 - 22:49:05 CEST