Re: The naive test for equality

vc wrote:

>> <Paul> wrote:
>> "well, the equivalence class can be thought of as a set of possible
>> representations for the "value" that "is" the equivalence class "

maybe you're readng more into it than I mean.

Probably a concrete example might best explain what I'm trying to say.

Consider simple fractions. You have several ways of writing the number 0.5, for example 1/2, 2/4, 3/6, etc. (infinitely many in fact). I'm just saying that all these are possible ways of representing the same number or "value".

You gave the details of how the rationals are constructed mathematically using equivalence relations. In practice, you aren't going to write the rational number 0.5 as the set (1/2, 2/4, 3/6, ...), you will pick one example and use that. In think the standard notation used is square brackets e.g. [1/2] to denote the equivalence class to which 1/2 belongs. Or you could just as well use [2/4].

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.

When we write 1/2 or 2/4 it is just shorthand for "[1/2]" or "the equivalence class containing 1/2" so 1/2 and 2/4 are actually identical at some level. But clearly at the level of marks on paper or bytes on a computer they are different. And these two levels correspond to the physical and logical levels of the relational model. So something can be equal at the logical level but different at the physical level.

Am I just stating the obvious in a very roundabout way? The orginal post gave an example of strings with a definition of equality that made anagrams equal to each other. The claim was made that that wasn't a proper example because it was an equivalence relation rather than a "plain" equality and I'm just rebutting that claim. I think that was the whole point of this somewhat rambling post.

Slightly confusing the issue is the fact that we are using the word "relation" in a mathematical rather than database sense here.

Paul. Received on Sat Aug 06 2005 - 16:54:36 CEST