Re: The naive test for equality


"Paul" <paul@xxxxxxxx> wrote in message
news:42f12830$0$24039$ed2619ec@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> 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.
>
>


.

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