Re: The naive test for equality

Paul wrote:
> Marshall Spight wrote:
> >>I've kind of lost track of what started this thread in the first place
> >>now! I think it was just to say I didn't think there was any real
> >>difference between equality and equivalence relations. Each one defines
> >>the other.
> >
> > Equality is a particular type of equivalence relation. It is the kind
> > where every value is its own equivalence class. Put another way,
> > in equality, the equivalence classes all have cardinality 1.
>
> That's not how I interpret it. The way I see it, an equivalence relation
> *defines* what we mean by equality with respect to a given structure.

I suppose. We're not quite talking about the same thing, though. I'm talking about classes of values, and you're talking about classes of lexical representations of values. Or maybe you're talkin about expressions; I'm not entirely certain.

(Does the string-of-symbols "one half" also belong in the equivalence class with "1/2" and "2/4"?)

I think it is more useful to think about 1/2 and 2/4 being the same value because of the semantics of division. Once you move into the world of values and out of the world of representations, things get a lot simpler.

Marshall Received on Sat Aug 06 2005 - 23:23:02 CEST