Re: Objects and Relations

On Feb 23, 6:46 am, "Alfredo Novoa" <alfred..._at_gmail.com> wrote:
> On 23 feb, 09:57, "Cimode" <cim..._at_hotmail.com> wrote:
>
> > RM theory uses *relation* in its primal mathematical sense not in a
> > general common sense.
>
> The mathematical definition is just a formalization of the "general
> common sense".
>
> > To RM advocates, a relation is not a
> > *relationship* synonym
>
> Relation and relationship are synonyms.
>
> Regards

Maybe the following example can be helpful to clarifies "general common sense" in the mathematical definition of Relation:

(i)

Let R be a relation given with the following table :

R | a b c

    |
b | T T F

    |
c | F F T

(ii)

Let A = {a, b, c}

Then we can show that R given in (i)
now is an equivalence relation on A
For example:
The truth value of ( bRa AND aRc => bRc) is T

In case (i) I didn't mentioned any set. Relation R is not defined on a set, and it is not a set.
Rather it is a statement with two free variables. In case (ii) R is defined for the members of set A. Even more R generates subsets of A, its equivalence classes.

Vladimir Odrljin Received on Sat Mar 03 2007 - 20:48:12 CET