Obsolesence of <>

[David C. Ullrich]

On Sun, 03 Jun 2001 06:52:52 GMT, "Nick Perkins" <nperkins7 at home.com>
wrote:

>In defense of Jose, i think he was trying to provide
>a 'total order relation' on the complex numbers,
>whereas the 'simple' method is a 'partial order relation'.
>
>The difference would be that in a total order relation,
>no two different complexes would map to the same real,
>so no two different complexes would compare as 'equal'.
>
>I am not sure is Jose succeeds, or if that is even possible.
>I seem to remember that it is possible,...i think...

It's certainly possible to define a total order on the
complex numbers, for example by comparing tuples
lexicographically (as I gather was suggested).

What's not possible is to define a total order on
the complexes that will make the complexes into
what's called an "ordered field" - that's a field
with an order (so far ok) with certain compatibility
requirements between the field structure and the
order.

>Personally, i would compare complex numbers by their
>distance to the origin ( in the 2D complex plane ).
>This could be optimized by directly comparing the
>sum of sqaures of the real and imag parts, without
>bothering to do the sqrt to find the actual distance
>to the origin.

But _this_ does not define a total order on the complexes
because different complexes do compare the same.


David C. Ullrich
*********************
"Sometimes you can have access violations all the 
time and the program still works." (Michael Caracena, 
comp.lang.pascal.delphi.misc 5/1/01)