Re: Testing for the equivalence relation

"Dan" <guntermann_at_verizon.net> wrote in message news:1120240628.808945.261440_at_g47g2000cwa.googlegroups.com...
> Thank you Jan.
>
> Another counter example that now seems so obvious in hindsight.
>
> So this leads me to my real objective. I now am wondering how we apply
> this to a relational model of data, or to what degree it is applicable
> without modification? I have quite a few question, but I'll try to
> focus on only one for now.
>
> Suppose I define an alphabet A to be the the set of symbols {'a', 'b',
> 'c', 'd', 'e'}, and the set of strings S over A consisting of the set
> of 1-tuples such that formal language is defined as {'a', 'b', 'c',
> 'd', 'e'}. We can also refer to S as a domain S in some universe of
> discourse.
>
> Further suppose that a binary relation is defined over S, is given as
> R(u: S, v: S); and we claim that it is an equivalence relation, and it
> has the following extensional value:
>
> u v
> -- --
> a a
> b b
> c c
> d d
> a b
> b a
> c d
> d c
>
> Here there are 4 equivalence classes and two distinct equivalence
> classes.

There are just two equivalence classes. What's a 'distinct' equivalence class ? Is it some kind of 'computer'-math speak ?

Saw your later comment. Since an equivalence class is a subset of the original set over which the equivalence relation is defined, how the {a,b} subset is different from the {a, b} subset ?

vc Received on Sun Jul 03 2005 - 06:19:25 CEST