Re: The naive test for equality

"Paul" <paul_at_test.com> wrote in message news:42f12830$0$24039$ed2619ec_at_ptn-nntp-reader01.plus.net...
> VC wrote:
>> Then rationals are a set Q of equivalence classes defined by the above
>> relation. Technically, one has to *prove* that E is indeed an
>> equivalence
>> relations and that operations like addition and multiplication are well
>> defined and obey the usual laws, etc.
>>
>> There is no neeed to talk about some vague representations and such, one
>> can simply speak in clear terms of integers and equivalence classes
>> instead.
>
> well, the equivalence class can be thought of as a set of possible
> representations for the "value" that "is" the equivalence class (feeling
> like Clinton here explaining what I mean by "is" :))

The usual definition of the equivalence class goes is:

Let E be an equivalence relation on the set S. Then, for a given element e in S, its equivalence class is a set of all elements in S that are equivalent to e:

[e] = {x in S| x E e}.

I have no idea what a 'possible representation' might be.

>
> By "representation" I mean the actual symbols used to convey the idea of
> a "value", and they may be several of these representations for one value.
>

I do not understand this.

> Paul.
>
>
Received on Thu Aug 04 2005 - 04:48:27 CEST