Re: The naive test for equality
Date: 8 Aug 2005 09:01:30 -0700
Message-ID: <1123516890.932363.109840_at_f14g2000cwb.googlegroups.com>
David Cressey wrote:
>
> Right. The entire equivalence class is a single element as viewed by the
> rationals engine.
> In order to manipulate this "single element" as data, we need a symbol for
> it, to represent it.
>
> So we choose one of the elements of the original set to stand as a
> representative of the entire set that is going to be seen as an element. In
> this case we might choose the rational with the lowest denominater, namely
> 1/2.
>
> Now, whenever we are given an unnormalized rational, such as 5/10, we ask
> the rationals engine to normalize it for us.
> The rationals engine knows the rule for normalizing, namely remove common
> factors in the numerator and denominator. So it returns 1/2, the
> normalized equivalent of 5/10.
>
> If we ask the rationals engine to normalize 1/2, it will give us back 1/2.
>
> So the process of normalizing is choosing one, out of an equivalence class,
> according to some criterion, and using the symbol that represents the
> chosen element to act as the normalized form for the entire class.
I also don't see the benefit of talking about separate engines.
Marshall Received on Mon Aug 08 2005 - 18:01:30 CEST