(in)exactness of complex numbers

[Michael Abbott]

ullrich at math.okstate.edu (David C. Ullrich) wrote in
news:3b71404b.1075769 at nntp.sprynet.com: 

> On Wed, 8 Aug 2001 08:46:17 +0000 (UTC), Michael Abbott
> <michael at rcp.co.uk> wrote:
>>
>>No, no, it's not impossible at all.  You simply use one representative
>>at a time to represent a value, but use the relation when you need to
>>decide whether or not two values are equal. 
> 
> Of course. I _said_ that. You _quote_ part of where I said that
> below.
>>
>>> Here there _is_ a natural choice of one polynomial to use
>>> from each equivalence class, but if you use that one your complex
>>> numbers have become precisely pairs of reals. 
>>

Well, but it's not quite the same thing.  I was saying that *in general* 
you can represent equivalence classes by members, even if you can't choose 
a canonical representative of each class.  Of course, when you *can* chose 
such a representative then things are much easier!

(I'm studying rewriting at the moment, and this business of finding 
canonical representatives, "normal forms", is rather central!)

> 
> (Doesn't matter, though - we have a special diss-pensation for
> off-topic posts. Um, <wink>...)

;)  Yes, I think we've drifted away from Python (and complex numbers) 
somewhat.  Never mind, it's quite entertaining over here anyhow. ;/